%%% BIB file for latex: all my refs on q. chaos, eigenmode problems, num anal.
%%%
%%%  Barnett 4/14/06

Note comments don't use % character; anything outside an (AT){...} is a comment

@STRING{ prl = "Phys. Rev. Lett." }
@STRING{ epl = "Europhys. Lett." }
@STRING{ pra = "Phys. Rev. A" }
@STRING{ prb = "Phys. Rev. B" }
@STRING{ prc = "Phys. Rev. C" }
@STRING{ prd = "Phys. Rev. D" }
@STRING{ pre = "Phys. Rev. E" }
@STRING{ jpa = "J. Phys. A" }
@STRING{ jpb = "J. Phys. B" }
@STRING{ jpc = "J. Phys. C" }
@STRING{ pa  = "Physica A" }
@STRING{ pb  = "Physica B" }
@STRING{ pc  = "Physica C" }
@STRING{ pd  = "Physica D" }
@STRING{ npa = "Nucl. Phys. A" }
@STRING{ npb = "Nucl. Phys. B" }
@STRING{ revmod = "Rev. Mod. Phys." }
@STRING{ prep   = "Phys. Rep." }
@STRING{ proy   = "Proc. R. Soc. Lond." }
@STRING{ anphys = "Ann. Phys." }
@STRING{ jmp  = "J. Math. Phys." }
@STRING{ jchem  = "J. Chem. Phys." }
@STRING{ jpchem = "J. Phys. Chem." }
@STRING{ plett  = "Phys. Lett." }
@STRING{ nonlin = "Nonlinearity" }
@STRING{ commun = "Commun. Math. Phys." }
@STRING{ cpam = "Comm. Pure Appl. Math." }
@STRING{ cpc = "Comput. Phys. Commun." }
@STRING{ jcp = "J. Comput. Phys." }
@STRING{ sirev = "SIAM Review" }
@STRING{ sinum = "SIAM J. Numer. Anal." }
@STRING{ sisc = "SIAM J. Sci. Comp." }
@STRING{ oe = "Opt. Express" }
@STRING{ ao = "Appl. Optics" }
@STRING{ mmas = "Math. Meth. Appl. Sci." }
@STRING{ bit = "BIT Numer. Math." }


% ----------------------------------------------- some of my publications

@article{dil,
author={A. H. Barnett and D. Cohen and E. J. Heller},
title={Deformations and dilations of chaotic billiards:
dissipation rate, and quasi-orthogonality of the boundary wavefunctions},
journal=prl,
volume={85},
pages={1412},
year=2000
}
%note={{\tt http://arxiv.org/nlin.CD/0003018}}

@article{pnm,
author = {Cohen, Doron and Barnett, Alex and Heller, Eric J.},
title = {Parametric evolution for a deformed cavity},
journal = pre,
volume = {63},
pages = {046207},
year=2001,
note={{\tt http://arxiv.org/nlin.CD/0008040}}
}

@article {wlf,
    AUTHOR = {Barnett, Alex and Cohen, Doron and Heller, Eric J.},
     TITLE = {Rate of energy absorption for a driven chaotic cavity},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {34},
      YEAR = {2001},
    NUMBER = {3},
     PAGES = {413--437},
     CODEN = {JPHAC5},
   MRCLASS = {81Q50},
  MRNUMBER = {MR1822784 (2002a:81069)},
note={{\tt http://arxiv.org/nlin.CD/0006041}}
}

@phdthesis{mythesis,
author={Barnett, A. H.},
title={Dissipation in deforming chaotic billiards},
school={Harvard University},
year={2000},
note={available at \verb+http://www.math.dartmouth.edu/~ahb/thesis_html/+}
}

@article{que,
author = "Barnett, A. H.",
title = "Asymptotic rate of quantum ergodicity in chaotic {E}uclidean
billiards",
year = {2006},
journal = cpam,
volume = 59,
number= 10,
pages = {1457--88}
}
%note = "\url{http://arxiv.org/math-ph/0512030}"

%note="13 pages, {\tt nlin.CD/0611059}",
@article{mush,
author="Barnett, A. H. and Betcke, T.",
title="Quantum mushroom billiards",
volume=17,
journal="CHAOS",
pages=043125,
year="2007",
}

@misc{quasi,
author = "Barnett, A. H.",
title = "Quasi-orthogonality on the boundary for {E}uclidean {L}aplace
eigenfunctions",
note = "{\em preprint}, {\tt math-ph/0601006}, available at
{\tt http://arxiv.org}"
}

@misc{sca,
author = "Barnett, A. H. and Hassell, A.",
title = "Fast computation of high frequency {D}irichlet eigenmodes via the spectral flow of the interior {N}eumann-to-{D}irichlet map",
note = "in press, {\em Comm. Pure Appl. Math.}, 2012."
}

@article{incl,
author="Barnett, A. H.",
title="Perturbative analysis of the {M}ethod of {P}articular {S}olutions
for improved inclusion of high-lying {D}irichlet eigenvalues",
journal=sinum,
year=2009,
volume=47,
number=3,
pages={1952--1970},
}

@article{polygonscatt,
author="Barnett, A. H. and Betcke, T.",
title="An exponentially convergent non-polynomial finite element
method for time-harmonic scattering from polygons",
journal=sisc,
volume=32,
number=3,
pages={1417--1441},
year=2010
}

@misc{mpspack,
author="Barnett, A. H. and Betcke, T.",
title="{\verb+MPSpack+}: A {MATLAB} toolbox to solve {H}elmholtz {PDE}, wave scattering, and eigenvalue problems using particular solutions and integral equations. [computer software]",
note={version 1.2. Available at \verb+http://code.google.com/p/mpspack/+},
year=2011
}


%note="{\tt arXiv:0708.3533 [math.NA]}",
@article{mfs,
author="Barnett, A. H. and Betcke, T.",
title="Stability and convergence of the {M}ethod of {F}undamental {S}olutions
for {H}elmholtz problems on analytic domains",
year=2008,
journal=jcp,
volume="227",
number="14",
pages={7003--7026}
}

@article{recon,
author = "Moorcroft, P. R. and Barnett, A. H.",
title = "Mechanistic home range models and resource selection analysis: a reconciliation and unification",
volume = "89",
year = {2008},
number=4,
pages={1112--1119},
journal = "Ecology",
note="{\tt arXiv:q-bio/0612008}"
}

@article{exact,
author = "Barnett, A. H and Moorcroft, P. R.",
title = "Analytic steady-state space use patterns
and rapid computations in mechanistic home range analysis",
volume = "57",
number=1,
pages={139--159},
year = {2008},
journal = "J. Math. Biol.",
note="{\tt arXiv:0705.3473 [q-bio.QM]}"
}

@article{custo,
author="Custo, A. and Wells III, W. M. and Barnett, A. H. and Hillman, E. M. C. and Boas, D. A.",
title="Effective scattering coefficient of the cerebral spinal fluid in adult head models for Diffuse Optical Imaging",
journal="Appl. Opt.",
volume=45,
pages={4747--4755},
year=2006
}

@article{aob,
author="Barnett, A. H. and Culver, J. P and Sorensen, A. G. and Dale, A. and Boas, D. A.",
title="Robust inference of baseline optical properties of the human head with
{3D} segmentation from magnetic resonance imaging",
journal="Appl. Opt.",
year=2003,
volume=42,
pages={3095--3108}
}

@article{sla,
author="Barnett, A. H.",
title="A fast numerical method for time-resolved photon diffusion in general stratified turbid media",
journal=jcp,
year=2004,
volume=201,
pages={771-797}
}

% fix the capital in the title here...........................
@article{notams08,
author="Barnett, A. H.",
title={Cover image of chaotic modes numbered
$10^n$ where $n=0,1\ldots 5$, accompanying the article
{\it {W}hat is quantum chaos?} by {Z.~Rudnick}},
journal="Notices Amer. Math. Soc.",
year=2008,
month="January"
}

@article{qplp,
author="A H Barnett and L Greengard",
title="A new integral representation for quasi-periodic fields
and its application to two-dimensional band structure calculations",
journal=jcp,
year=2010,
volume=229,
pages={6898--6914}
}

@article{qpsc,
author="A H Barnett and L Greengard",
title="A new integral representation for quasi-periodic scattering
problems in two dimensions",
journal=bit,
year=2011,
volume=51,
pages={67--90}
}

@article{tenney,
author={Larry Polansky and Alex Barnett and Michael Winter},
title="A Few More Words About {J}ames {T}enney:
Dissonant Counterpoint and Statistical Feedback",
journal="J. Math. Music",
volume=5,
number=2,
pages={63--82},
year=2011
}

%note={\verb+http://arXiv.org/abs/1006.3592v1+}
@article{bnds,
title="Boundary quasi-orthogonality and sharp inclusion bounds for large {D}irichlet eigenvalues",
author="A. H. Barnett and Andrew Hassell",
journal="SIAM J. Numer. Anal.",
year=2011,
volume=49,
pages={1046--1063}
}

@inproceedings{neubnds,
title={Estimates on {N}eumann eigenfunctions at the boundary, and the ``{M}ethod of {P}articular {S}olutions'' for computing them},
author="A. H. Barnett and Andrew Hassell",
year=2012,
pages={196--210},
booktitle={Spectral Geometry, proceedings of the 2010 International Conference on Spectral Geometry, Dartmouth College}
}

@misc{QBX,
title={Quadrature by expansion:
a new method for the evaluation of layer potentials},
author={A. Kl\"ockner and A. H. Barnett and L. Greengard and M. O'Neil},
year=2012,
journal=jcp,
note={submitted}
}



% ----------------------------------------- dynamical systems, classical chaos

@article {stadium,
    AUTHOR = {Bunimovich, L. A.},
     TITLE = {Conditions of stochasticity of two-dimensional billiards},
   JOURNAL = {CHAOS},
  FJOURNAL = {CHAOS. An Interdisciplinary Journal of Nonlinear Science},
    VOLUME = {1},
      YEAR = {1991},
    NUMBER = {2},
     PAGES = {187--193},
      CODEN = {CHAOEH},
   MRCLASS = {58F11},
  MRNUMBER = {MR1135907 (92h:58113)},
MRREVIEWER = {Valery Covachev},
}

@book {gutz,
    AUTHOR = {Gutzwiller, Martin C.},
     TITLE = {Chaos in classical and quantum mechanics},
    SERIES = {Interdisciplinary Applied Mathematics},
    VOLUME = {1},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1990},
     PAGES = {xiv+432},
     MRCLASS = {58F13 (34C35 58F05 70H05 70K50 81Q50)},
  MRNUMBER = {MR1077246 (91m:58099)},
MRREVIEWER = {N. L. Balazs},
}

@article {disperse,
    AUTHOR = {Sina{\u\i}, {Ya}. G.},
     TITLE = {Dynamical systems with elastic reflections. {E}rgodic
              properties of dispersing billiards},
   JOURNAL = {Uspehi Mat. Nauk},
  FJOURNAL = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo.
              Uspekhi Matematicheskikh Nauk},
    VOLUME = {25},
      YEAR = {1970},
    NUMBER = {2 (152)},
     PAGES = {141--192},
     MRCLASS = {28.70},
  MRNUMBER = {MR0274721 (43 \#481)},
MRREVIEWER = {V. Drobot},
}

@article{whatbil,
author = {Sina{\u\i}, {Ya}. G.},
title = {{WHAT IS}\ldots a billiard?},
journal = {Notices Amer. Math. Soc.},
volume={51},
year={2004},
number=4,
pages={412--413}
}


@article {mushroom,
author = {Bunimovich, L. A.},
   JOURNAL = {CHAOS},
  FJOURNAL = {CHAOS. An Interdisciplinary Journal of Nonlinear Science},
title = "Mushrooms and other billiards with divide phase space",
year=2001,
volume=11,
number=4,
month={December}
}

@article{porter,
author = {Porter, Mason A. and Lansel, Steven},
journal = {Notices Amer. Math. Soc.},
title = {Mushroom billiards},
volume={53},
number={3},
pages={334--337},
year = {2006}
}

@article {sticky1,
    AUTHOR = {Altmann, Eduardo G. and Motter, Adilson E. and Kantz, Holger},
     TITLE = {Stickiness in mushroom billiards},
   JOURNAL = {CHAOS},
  FJOURNAL = {CHAOS. An Interdisciplinary Journal of Nonlinear Science},
    VOLUME = {15},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {033105, 7},
        CODEN = {CHAOEH},
   MRCLASS = {37J10 (37J40 70H05 70K55)},
  MRNUMBER = {MR2184869 (2006e:37095)}
}
%note={\url{http://arxiv.org/nlin.CD/0502058}}

@article{sticky2,
author = {Eduardo G. Altmann and Adilson E. Motter and Holger Kantz},
collaboration = {},
title = {Stickiness in Hamiltonian systems: From sharply divided to hierarchical phase space},
publisher = {APS},
year = {2006},
journal = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)},
volume = {73},
number = {2},
eid = {026207},
numpages = {10},
pages = {026207},
keywords = {chaos},
}
%url = {http://link.aps.org/abstract/PRE/v73/e026207}

@article {rauch,
    AUTHOR = {Rauch, Jeffrey},
     TITLE = {Illumination of bounded domains},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {85},
      YEAR = {1978},
    NUMBER = {5},
     PAGES = {359--361},
    MRCLASS = {52A10},
  MRNUMBER = {MR0482537 (58 \#2603)},
MRREVIEWER = {H. T. Croft},
}







% --------------------------------------------------- quantum ergodicity, QUE

@article {cdv,
    AUTHOR = {Colin de Verdi{\`e}re, Y.},
     TITLE = {Ergodicit\'e et fonctions propres du laplacien},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {102},
      YEAR = {1985},
    NUMBER = {3},
     PAGES = {497--502},
        CODEN = {CMPHAY},
   MRCLASS = {58G25 (35P20)},
  MRNUMBER = {MR818831 (87d:58145)},
MRREVIEWER = {J{\"u}rgen Eichhorn},
}

@article{schnir,
author={A. I. Schnirelman},
title={Ergodic properties of eigenfunctions},
journal={Usp. Mat. Nauk.},
volume={29},
pages={181},
year={1974}
}

@article {zel,
    AUTHOR = {Zelditch, Steven},
     TITLE = {Uniform distribution of eigenfunctions on compact hyperbolic
              surfaces},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {55},
      YEAR = {1987},
    NUMBER = {4},
     PAGES = {919--941},
       CODEN = {DUMJAO},
   MRCLASS = {58G25 (58G30)},
  MRNUMBER = {MR916129 (89d:58129)},
MRREVIEWER = {Alejandro Uribe},
}

@article {aurich,
    AUTHOR = {Aurich, R. and Taglieber, M.},
     TITLE = {On the rate of quantum ergodicity on hyperbolic surfaces and
              for billiards},
   JOURNAL = {Phys. D},
  FJOURNAL = {Physica D. Nonlinear Phenomena},
    VOLUME = {118},
      YEAR = {1998},
    NUMBER = {1-2},
     PAGES = {84--102},
        CODEN = {PDNPDT},
   MRCLASS = {81Q50 (58F11)},
  MRNUMBER = {MR1629251 (99f:81055)},
MRREVIEWER = {Jens Marklof},
}

@article {zonb2,
    AUTHOR = {Zelditch, Steven},
     TITLE = {A random matrix model for quantum mixing},
   JOURNAL = {Internat. Math. Res. Notices},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {115--137},
     MRCLASS = {81Q50 (58G15)},
  MRNUMBER = {MR1383753 (97j:81085)},
MRREVIEWER = {Jens Bolte},
}       % note there's no volume; it's "volume 1996" according to Hindawi.

@article {zeloffdiagque,
    AUTHOR = {Zelditch, Steve},
     TITLE = {Note on quantum unique ergodicity},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {132},
      YEAR = {2004},
    NUMBER = {6},
     PAGES = {1869--1872 (electronic)},
      CODEN = {PAMYAR},
   MRCLASS = {58J50 (35P05 35Q40 58J40)},
  MRNUMBER = {MR2051153 (2005i:58039)},
MRREVIEWER = {Jonathan Huntley},
note={\url{http://arxiv.org/math-ph/0301035}}
}

@article {zqmix,
    AUTHOR = {Zelditch, Steven},
     TITLE = {Quantum mixing},
   JOURNAL = {J. Funct. Anal.},
  FJOURNAL = {Journal of Functional Analysis},
    VOLUME = {140},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {68--86},
        CODEN = {JFUAAW},
   MRCLASS = {58G25 (58G18 81Q20 82B10)},
  MRNUMBER = {MR1404574 (98f:58197)},
}

@incollection{zencyc,
author={Zelditch, Steven},
title={Quantum ergodicity and mixing of eigenfunctions},
booktitle={Elsevier Encyclopedia of Mathematical Physics},
publisher={Academic Press},
pages={183--196},
volume=1,
note={{\tt arXiv:math-ph/0503026}},
year={2006}
}

@article {zzw,
    AUTHOR = {Zelditch, Steven and Zworski, Maciej},
     TITLE = {Ergodicity of eigenfunctions for ergodic billiards},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {175},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {673--682},
        CODEN = {CMPHAY},
   MRCLASS = {58G25 (58F11 58G15)},
  MRNUMBER = {MR1372814 (97a:58193)},
MRREVIEWER = {Edoh Amiran},
}

@article {baecker,
    AUTHOR = {B{\"a}cker, A. and Schubert, R. and Stifter, P.},
     TITLE = {Rate of quantum ergodicity in {E}uclidean billiards},
   JOURNAL = {Phys. Rev. E (3)},
  FJOURNAL = {Physical Review E. Statistical, Nonlinear, and Soft Matter
              Physics},
    VOLUME = {57},
      YEAR = {1998},
    NUMBER = {5, part A},
     PAGES = {5425--5447},
       CODEN = {PLEEE8},
   MRCLASS = {81Q50 (58F11)},
  MRNUMBER = {MR1626188 (99f:81056a)},
MRREVIEWER = {Jens Marklof},
note={also see Errata for this paper,
{\em Phys. Rev. E}, 58 (4) (1998)}
}

@article {backerbdry,
    AUTHOR = {B{\"a}cker, A. and F{\"u}rstberger, S. and Schubert, R.
              and Steiner, F.},
     TITLE = {Behaviour of boundary functions for quantum billiards},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {35},
      YEAR = {2002},
    NUMBER = {48},
     PAGES = {10293--10310},
       CODEN = {JPHAC5}
}
%   MRCLASS = {81Q50 (35P20)},
%  MRNUMBER = {MR1947308 (2003j:81065)},
%MRREVIEWER = {Jens Marklof},

 


@article {bogarith,
    AUTHOR = {Bogomolny, E. B. and Georgeot, B. and Giannoni, M.-J. and
              Schmit, C.},
     TITLE = {Chaotic billiards generated by arithmetic groups},
   JOURNAL = {Phys. Rev. Lett.},
  FJOURNAL = {Physical Review Letters},
    VOLUME = {69},
      YEAR = {1992},
    NUMBER = {10},
     PAGES = {1477--1480},
        CODEN = {PRLTAO},
   MRCLASS = {81Q50 (20H15 58F17 82B05)},
  MRNUMBER = {MR1178884 (93g:81025)},
}

@article {donnelly,
    AUTHOR = {Donnelly, Harold},
     TITLE = {Quantum unique ergodicity},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {131},
      YEAR = {2003},
    NUMBER = {9},
     PAGES = {2945--2951 (electronic)},
       CODEN = {PAMYAR},
   MRCLASS = {58J50},
  MRNUMBER = {MR1974353 (2005a:58048)},
}

@article {linden,
    AUTHOR = {Lindenstrauss, Elon},
     TITLE = {Invariant measures and arithmetic quantum unique ergodicity},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {163},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {165--219},
        CODEN = {ANMAAH},
   MRCLASS = {11Kxx (22Exx 37Axx)},
  MRNUMBER = {MR2195133},
}

@book {martinez,
    AUTHOR = {Martinez, Andr{\'e}},
     TITLE = {An introduction to semiclassical and microlocal analysis},
    SERIES = {Universitext},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2002},
     PAGES = {viii+190},
     MRCLASS = {35A27 (35-01 35Q40 35S05 47G30 58J15 58J40)},
  MRNUMBER = {MR1872698 (2003b:35010)},
MRREVIEWER = {Peter D. Hislop},
}

@article {tate,
    AUTHOR = {Tate, Tatsuya},
     TITLE = {Some remarks on the off-diagonal asymptotics in quantum
              ergodicity},
   JOURNAL = {Asymptot. Anal.},
  FJOURNAL = {Asymptotic Analysis},
    VOLUME = {19},
      YEAR = {1999},
    NUMBER = {3-4},
     PAGES = {289--296},
          CODEN = {ASANEZ},
   MRCLASS = {58J37 (35P20 35S99 37D20 37J99 58J40 58J50)},
  MRNUMBER = {MR1696219 (2000d:58041)},
MRREVIEWER = {G. V. Rozenblyum},
}

 @article {zonb1,
    AUTHOR = {Zelditch, Steven},
     TITLE = {Quantum ergodicity on the sphere},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {146},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {61--71},
        CODEN = {CMPHAY},
   MRCLASS = {58G25 (58F17 81Q50)},
  MRNUMBER = {MR1163667 (93e:58191)},
MRREVIEWER = {Alejandro Uribe},
}

@article {zelupper,
    AUTHOR = {Zelditch, Steven},
     TITLE = {On the rate of quantum ergodicity. {I}. {U}pper bounds},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {160},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {81--92},
         CODEN = {CMPHAY},
   MRCLASS = {58G25 (35P20 58F17 58G15)},
  MRNUMBER = {MR1262192 (95f:58084)},
MRREVIEWER = {Alejandro Uribe},
}

@article {zellower,
    AUTHOR = {Zelditch, Steven},
     TITLE = {On the rate of quantum ergodicity. {II}. {L}ower bounds},
   JOURNAL = {Comm. Partial Differential Equations},
  FJOURNAL = {Communications in Partial Differential Equations},
    VOLUME = {19},
      YEAR = {1994},
    NUMBER = {9-10},
     PAGES = {1565--1579},
          CODEN = {CPDIDZ},
   MRCLASS = {58G25 (58F17 58G15)},
  MRNUMBER = {MR1294471 (96e:58161)},
MRREVIEWER = {U. Hamenst{\"a}dt},
}

@article {hassell,
    AUTHOR = {Hassell, Andrew and Zelditch, Steve},
     TITLE = {Quantum ergodicity of boundary values of eigenfunctions},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {248},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {119--168},
     CODEN = {CMPHAY}
}
%   MRCLASS = {35P05 (35J05 37N20 47G30 58J37 58J40)},
%  MRNUMBER = {MR2104608 (2005h:35255)},
%MRREVIEWER = {Sergey G. Pyatkov},

@article {marklof,
    AUTHOR = {Marklof, Jens and O'Keefe, Stephen},
     TITLE = {Weyl's law and quantum ergodicity for maps with divided phase
              space},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {18},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {277--304},
       CODEN = {NONLE5},
   MRCLASS = {81Q50 (37A05 37D50 37N20)},
  MRNUMBER = {MR2109478 (2006b:81086)},
MRREVIEWER = {Dieter H. Mayer},
}

@article{percival,
author={Percival, I. C.},
year={1973},
title={Regular and irregular spectra},
journal=jpb,
pages={L229--232}
}

@incollection {zelinvspec,
    AUTHOR = {Zelditch, Steve},
     TITLE = {Inverse resonance problem for {$\Bbb Z\sb 2$}-symmetric
              analytic obstacles in the plane},
 BOOKTITLE = {Geometric methods in inverse problems and PDE control},
    SERIES = {IMA Vol. Math. Appl.},
    VOLUME = {137},
     PAGES = {289--321},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2004},
   MRCLASS = {58Jxx (35P20 35R30)},
  MRNUMBER = {MR2169909},
}

@article {soggegrowth,
    AUTHOR = {Sogge, Christopher D. and Zelditch, Steve},
     TITLE = {Riemannian manifolds with maximal eigenfunction growth},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {114},
      YEAR = {2002},
    NUMBER = {3},
     PAGES = {387--437},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {58J50 (35P20)},
  MRNUMBER = {MR1924569 (2004b:58053)},
MRREVIEWER = {Tatyana E. Foth},
}


@article{landry,
author={Landry, Brian and Heller, Eric J.},
title={Statistical Properties of Many Particle Eigenfunctions},
journal={J. Phys. A},
volume=40,
pages={9259--74},
year={2007},
}
%note={preprint, \url{http://arxiv.org/abs/0704.1881}}


@article{burqbb,
title="Bouncing ball modes and quantum chaos",
author="Burq, N. and Zworski, M.",
year=2005,
journal="SIAM Review",
volume=47,
issue=1,
pages={43--49}
}

@article{spreading,
title="Spreading of quasimodes in the {B}unimovich stadium",
author="Burq, N. and Hassell, A. and Wunsch, J.",
journal="Proc. Am. Math. Soc.",
year=2007,
volume=135,
pages={1029--1037}
}

@article{hassellBB,
author={A. Hassell},
title={Ergodic billiards that are not quantum unique ergodic. With an appendix by {A. Hassell} and {L. Hillairet}},
journal="Ann. Math.",
year=2010,
pages={605--618}, 
volume=171
}

@book{SafVas,
title="The Asymptotic Distribution of Eigenvalues of
Partial Differential Operators",
author="Yu Safarov and D Vassiliev",
year=1996,
publisher="American Mathematical Society, Providence, RI",
series="Translations of Mathematical Monographs \#155"
}

@article{Seeley,
title="An Estimate Near the Boundary for the Spectral Function of the {L}aplace Operator",
author="R Seeley",
year=1980,
journal="Amer. J. Math.",
volume=102,
number=5,
pages={869--902}
}

@article{Tataru,
author={D. Tataru},
title={On the regularity of boundary traces for the wave equation},
journal={Ann. Scuola Norm. Sup. Pisa Cl. Sci.},
volume={26},
number=1,
pages={185--206},
year={1998},
}

@article{Xu,
author={X. Xu},
title={Upper and lower bounds for normal derivatives of spectral clusters of {D}irichlet {L}aplacian},
journal={J. Math. Anal. Appl.},
year=2012,
volume=387,
number=1,
pages={374--383}
}
%note={available at \verb+http://arXiv.org/abs/1004.2517+}



@article{nonnenrev,
author={S Nonnenmacher},
title={Anatomy of quantum chaotic eigenstates},
journal={S\'eminaire Poincar\'e},
year=2010,
volume={XIV},
pages={177--220}
}



% ------------------------------------------------------------ automorphic

@article {lsquad,
    AUTHOR = {Luo, Wenzhi and Sarnak, Peter},
     TITLE = {Quantum variance for {H}ecke eigenforms},
   JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
              Quatri\`eme S\'erie},
    VOLUME = {37},
      YEAR = {2004},
    NUMBER = {5},
     PAGES = {769--799},
       CODEN = {ASENAH},
   MRCLASS = {11F72 (11F25 11F66)},
  MRNUMBER = {MR2103474 (2005k:11101)},
MRREVIEWER = {Ze{\'e}v Rudnick},
}

@article {RS,
    AUTHOR = {Rudnick, Ze{\'e}v and Sarnak, Peter},
     TITLE = {The behaviour of eigenstates of arithmetic hyperbolic
              manifolds},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {161},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {195--213},
       CODEN = {CMPHAY},
   MRCLASS = {11F72 (11F32 11F37 81Q50)},
  MRNUMBER = {MR1266075 (95m:11052)},
MRREVIEWER = {Jens Bolte},
}

@incollection {sarnak95,
    AUTHOR = {Sarnak, Peter},
     TITLE = {Arithmetic quantum chaos},
 BOOKTITLE = {The Schur lectures (1992) (Tel Aviv)},
    SERIES = {Israel Math. Conf. Proc.},
    VOLUME = {8},
     PAGES = {183--236},
 PUBLISHER = {Bar-Ilan Univ.},
   ADDRESS = {Ramat Gan},
      YEAR = {1995},
   MRCLASS = {11F72 (11M41 81Q50)},
  MRNUMBER = {MR1321639 (96d:11059)},
MRREVIEWER = {Jens Bolte},
}

@incollection {sarnakCRM,
    AUTHOR = {Sarnak, Peter},
     TITLE = {Spectra and eigenfunctions of {L}aplacians},
 BOOKTITLE = {Partial differential equations and their applications
              (Toronto, ON, 1995)},
    SERIES = {CRM Proc. Lecture Notes},
    VOLUME = {12},
     PAGES = {261--276},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1997},
   MRCLASS = {58G25 (35J25 35P05 58F17 81Q50)},
  MRNUMBER = {MR1479252 (98i:58240)},
MRREVIEWER = {{\'E}ric Leichtnam},
}

 @article {baltimore,
    AUTHOR = {Sarnak, Peter},
     TITLE = {Spectra of hyperbolic surfaces},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {40},
      YEAR = {2003},
    NUMBER = {4},
     PAGES = {441--478 (electronic)},
        CODEN = {BAMOAD},
   MRCLASS = {11N75 (11F03 11F72 11R42 30F45 35P30)},
  MRNUMBER = {MR1997348 (2004f:11107)},
MRREVIEWER = {Stephen D. Miller},
}

@article {lindenstrauss,
    AUTHOR = {Lindenstrauss, Elon},
     TITLE = {Invariant measures and arithmetic quantum unique ergodicity},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {163},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {165--219},
       CODEN = {ANMAAH},
   MRCLASS = {11Kxx (22Exx 37Axx)},
  MRNUMBER = {MR2195133},
}


@inbook{arithrev,
author="Marklof, J.",
title="Arithmetic quantum chaos",
series="Encyclopedia of Mathematical Physics",
editors="Francoise, J.-P. and Naber G. L. and Tsou S.T.",
publisher="Elsevier, Oxford",
year=2006,
volume=1,
pages="212--220"
}






% ----------------------------------------------------------------- scars

@article {hel84,
    AUTHOR = {Heller, Eric J.},
     TITLE = {Bound-state eigenfunctions of classically chaotic
              {H}amiltonian systems: scars of periodic orbits},
   JOURNAL = {Phys. Rev. Lett.},
  FJOURNAL = {Physical Review Letters},
    VOLUME = {53},
      YEAR = {1984},
    NUMBER = {16},
     PAGES = {1515--1518},
       CODEN = {PRLTAO},
   MRCLASS = {81C25 (58F22)},
  MRNUMBER = {MR762412 (85k:81055)},
}

 
@incollection {hellerhouches,
    AUTHOR = {Heller, Eric J.},
     TITLE = {Wavepacket dynamics and quantum chaology},
 BOOKTITLE = {Chaos et physique quantique (Les Houches, 1989)},
     PAGES = {547--664},
 PUBLISHER = {North-Holland},
   ADDRESS = {Amsterdam},
      YEAR = {1991},
   MRCLASS = {81Q50 (58F13 81-02)},
  MRNUMBER = {MR1188425 (94i:81031)},
}

 @article {agam,
    AUTHOR = {Agam, Oded and Fishman, Shmuel},
     TITLE = {Semiclassical criterion for scars in wave functions of chaotic
              systems},
   JOURNAL = {Phys. Rev. Lett.},
  FJOURNAL = {Physical Review Letters},
    VOLUME = {73},
      YEAR = {1994},
    NUMBER = {6},
     PAGES = {806--809},
       CODEN = {PRLTAO},
   MRCLASS = {81Q50 (81-04 81-08)},
  MRNUMBER = {MR1285573 (95c:81028)},
}

@incollection{berryscar,
author="Berry, M. V.",
title={Some quantum-to-classical asymptotics},
pages={251--304},
     BOOKTITLE = {Chaos et physique quantique
(Les Houches Lecture Notes LII, 1989)},
 PUBLISHER = {North-Holland Publishing Co.},
editor = {M.-J. Giannoni and A. Voros and J. Zinn-Justin},
   ADDRESS = {Amsterdam},
      YEAR = {1991},
     MRCLASS = {81-06 (00B25 58-06 58F13)},
  MRNUMBER = {MR1188415 (93e:81003)},
}

@article {berryscar2,
    AUTHOR = {Berry, M. V.},
     TITLE = {Quantum scars of classical closed orbits in phase space},
   JOURNAL = {Proc. Roy. Soc. London Ser. A},
  FJOURNAL = {Proceedings of the Royal Society. London. Series A.
              Mathematical, Physical and Engineering Sciences},
    VOLUME = {423},
      YEAR = {1989},
    NUMBER = {1864},
     PAGES = {219--231},
      CODEN = {PRLAAZ},
   MRCLASS = {81S30 (58Z05 81Q50)},
  MRNUMBER = {MR1059234 (92c:81075)},
}

@article {bogscar,
    AUTHOR = {Bogomolny, E. B.},
     TITLE = {Smoothed wave functions of chaotic quantum systems},
   JOURNAL = {Phys. D},
  FJOURNAL = {Physica D. Nonlinear Phenomena},
    VOLUME = {31},
      YEAR = {1988},
    NUMBER = {2},
     PAGES = {169--189},
       CODEN = {PDNPDT},
   MRCLASS = {81C99 (58F13 81-04)},
  MRNUMBER = {MR955627 (89h:81062)},
}

@article {lev,
    AUTHOR = {Kaplan, L. and Heller, E. J.},
     TITLE = {Linear and nonlinear theory of eigenfunction scars},
   JOURNAL = {Ann. Physics},
  FJOURNAL = {Annals of Physics},
    VOLUME = {264},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {171--206},
       CODEN = {ADNYA6},
   MRCLASS = {81Q50},
  MRNUMBER = {MR1619193 (99f:81058)},
MRREVIEWER = {Julio Espinoza Ortiz},
}

@article {scarmometer,
    AUTHOR = {Kaplan, L. and Heller, E. J.},
     TITLE = {Measuring scars of periodic orbits},
   JOURNAL = {Phys. Rev. E (3)},
  FJOURNAL = {Physical Review E. Statistical, Nonlinear, and Soft Matter
              Physics},
    VOLUME = {59},
      YEAR = {1999},
    NUMBER = {6},
     PAGES = {6609--6628},
      CODEN = {PLEEE8},
   MRCLASS = {81Q50 (37N20)},
  MRNUMBER = {MR1695455 (2000b:81037)},
}

 


@article {faure,
    AUTHOR = {Faure, Fr{\'e}d{\'e}ric and Nonnenmacher, St{\'e}phane and De
              Bi{\`e}vre, Stephan},
     TITLE = {Scarred eigenstates for quantum cat maps of minimal periods},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {239},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {449--492},
       CODEN = {CMPHAY},
   MRCLASS = {81Q50 (37N20)},
  MRNUMBER = {MR2000926 (2005a:81076)},
}

 @article {li,
    AUTHOR = {Li, Baowen and Hu, Bambi},
     TITLE = {Statistical analysis of scars in stadium billiard},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {31},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {483--504},
      CODEN = {JPHAC5},
   MRCLASS = {81Q50},
  MRNUMBER = {MR1629174 (99b:81061)},
}

@article{schanz,
author={Schanz, H. and T. Kottos},
title={Scars on quantum networks ignore the
Lyapunov exponent},
journal=prl,
volume={90},
pages={234101},
year = {2003}
}

@article{spiralscar,
   author = {{Lee}, S.-Y. and {Rim}, S. and {Ryu}, J.-W. and {Kwon}, T.-Y. and 
	{Choi}, M. and {Kim}, C.-M.},
    title = "{Quasiscarred Resonances in a Spiral-Shaped Microcavity}",
  journal = prl,
   eprint = {nlin/0403025},
     year = 2004,
    month = oct,
   volume = 93,
   number = 16,
    pages = {164102-+},
}

@article{mortessagne,
author = {Mortessagne, F. and Legrand, O. and Sornette, D.},
title = "A geometric approach to wave dynamics in billiards",
journal = "Europhys. Lett.",
year=1996,
volume=33,
number=6,
pages={417--422}
}

@article{kudrolli,
author="Kudrolli, A. and Abraham, M. C. and Gollub, J. P.",
title="Scarred patterns in surface waves",
journal=pre,
year=2001,
volume=63,
pages=026208
}

@article{weeks,
author="Lehoucq, R. and Weeks, J. and Uzan, J.-P. and Gausmann, E. and Luminet, J. P.",
title="Eigenmodes of three-dimensional spherical spaces and their
application to cosmology",
journal="Class. Quantum Grav.",
year=2002,
volume=19,
pages={4683--4708}
}



% ----------------------------------------- chaotic matrix elements & FP

@article {fp86,
    AUTHOR = {Feingold, Mario and Peres, Asher},
     TITLE = {Distribution of matrix elements of chaotic systems},
   JOURNAL = {Phys. Rev. A (3)},
  FJOURNAL = {Physical Review. A. Third Series},
    VOLUME = {34},
      YEAR = {1986},
    NUMBER = {1},
     PAGES = {591--595},
       CODEN = {PLRAAN},
   MRCLASS = {81C15 (58F13)},
  MRNUMBER = {MR848319 (87i:81055)},
}

@article {wilk87,
    AUTHOR = {Wilkinson, Michael},
     TITLE = {A semiclassical sum rule for matrix elements of classically
              chaotic systems},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {20},
      YEAR = {1987},
    NUMBER = {9},
     PAGES = {2415--2423},
       CODEN = {JPHAC5},
   MRCLASS = {81C99 (58F40 81D30)},
  MRNUMBER = {MR895065 (89f:81071)},
MRREVIEWER = {H. Hogreve},
}

@article {combe2,
    AUTHOR = {Combescure, M. and Robert, D.},
     TITLE = {Semiclassical sum rules and generalized coherent states},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {36},
      YEAR = {1995},
    NUMBER = {12},
     PAGES = {6596--6610},
        CODEN = {JMAPAQ},
   MRCLASS = {81R30 (81Q20)},
  MRNUMBER = {MR1359645 (97d:81069)},
MRREVIEWER = {Thierry Ramond},
}

@ARTICLE{boose,
  author = {D. Boose and J. Main},
  title = {Distributions of Transition Matrix Elements in Classically Mixed   Quantum Systems},
  journal = {Physical Review E},
  volume = {60},
  pages = {2831},
  eprint = {chao-dyn/9905029},
  year = {1999}
}

@article{EFKAMM,
author = {Eckhardt, Bruno and Fishman, Shmuel and Keating, Jonathan
and Agam, Oded and Main, J\"{o}rg and M\"{u}ller, Kirsten},
  title = {Approach to ergodicity in quantum wave functions},
  eprint = {chao-dyn/9509017},
journal = pre,
volume = {52},
pages = {5893--5903},
  year = {1995}
}

@article {hort,
    AUTHOR = {Hortikar, Sanjay and Srednicki, Mark},
     TITLE = {Random matrix elements and eigenfunctions in chaotic systems},
   JOURNAL = {Phys. Rev. E (3)},
  FJOURNAL = {Physical Review E. Statistical, Nonlinear, and Soft Matter
              Physics},
    VOLUME = {57},
      YEAR = {1998},
    NUMBER = {6},
     PAGES = {7313--7316},
       CODEN = {PLEEE8},
   MRCLASS = {81Q50},
  MRNUMBER = {MR1628191 (99a:81045)},
}

 @article {prosen,
    AUTHOR = {Prosen, Toma{\v{z}}},
     TITLE = {Statistical properties of matrix elements in a {H}amilton
              system between integrability and chaos},
   JOURNAL = {Ann. Physics},
  FJOURNAL = {Annals of Physics},
    VOLUME = {235},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {115--164},
       CODEN = {ADNYA6},
   MRCLASS = {81Q50 (81S30)},
  MRNUMBER = {MR1294439 (95g:81040)},
MRREVIEWER = {Jens Bolte},
}

@article {zeloffdiag,
    AUTHOR = {Zelditch, Steven},
     TITLE = {Quantum transition amplitudes for ergodic and for completely
              integrable systems},
   JOURNAL = {J. Funct. Anal.},
  FJOURNAL = {Journal of Functional Analysis},
    VOLUME = {94},
      YEAR = {1990},
    NUMBER = {2},
     PAGES = {415--436},
       CODEN = {JFUAAW},
   MRCLASS = {58F19 (58G25 81Q99)},
  MRNUMBER = {MR1081652 (92b:58181)},
MRREVIEWER = {David Gurarie},
}

% ---------------------------------------------------- Wigner, Bargmann, Husimi

@article {bargmann1,
    AUTHOR = {Bargmann, V.},
     TITLE = {On a {H}ilbert space of analytic functions and an associated
              integral transform},
   JOURNAL = {Comm. Pure Appl. Math.},
  FJOURNAL = {Communications on Pure and Applied Mathematics},
    VOLUME = {14},
      YEAR = {1961},
     PAGES = {187--214},
     MRCLASS = {46.30},
  MRNUMBER = {MR0157250 (28 \#486)},
MRREVIEWER = {C. J. Eliezer},
}

@article {bargmann2,
    AUTHOR = {Bargmann, V.},
     TITLE = {On a {H}ilbert space of analytic functions and an associated
              integral transform. {P}art {II}. {A} family of related
              function spaces. {A}pplication to distribution theory},
   JOURNAL = {Comm. Pure Appl. Math.},
  FJOURNAL = {Communications on Pure and Applied Mathematics},
    VOLUME = {20},
      YEAR = {1967},
     PAGES = {1--101},
     MRCLASS = {46.30 (46.40)},
  MRNUMBER = {MR0201959 (34 \#1836)},
MRREVIEWER = {J. M. Jauch},
}



@article {stellar,
    AUTHOR = {Tualle, J.-M. and Voros, A.},
     TITLE = {Normal modes of billiards portrayed in the stellar (or nodal)
              representation},
   JOURNAL = {Chaos Solitons Fractals},
  FJOURNAL = {Chaos, Solitons and Fractals},
    VOLUME = {5},
      YEAR = {1995},
    NUMBER = {7},
     PAGES = {1085--1102},
      CODEN = {CSFOEH},
   MRCLASS = {58F19 (58F13 81Q50)},
  MRNUMBER = {MR1357264 (96g:58150)},
}

@article{carlo,
author = {Gabriel Carlo and Eduardo Vergini and Alejandro J. Fendrik},
collaboration = {},
title = {Numerical verification of Percival's conjecture in a quantum billiard},
publisher = {APS},
year = {1998},
journal = {Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics)},
volume = {57},
number = {5},
pages = {5397--5403},
keywords = {chaos; eigenvalues and eigenfunctions; quantum theory; fluctuations}
}
%url = {http://link.aps.org/abstract/PRE/v57/p5397}

@article {backerhus,
    AUTHOR = {B{\"a}cker, A. and F{\"u}rstberger, S. and Schubert, R.},
     TITLE = {Poincar\'e {H}usimi representation of eigenstates in quantum
              billiards},
   JOURNAL = {Phys. Rev. E (3)},
  FJOURNAL = {Physical Review E. Statistical, Nonlinear, and Soft Matter
              Physics},
    VOLUME = {70},
      YEAR = {2004},
    NUMBER = {3},
     PAGES = {036204, 10},
       CODEN = {PLEEE8},
   MRCLASS = {81Q50 (37N20 81S30)},
  MRNUMBER = {MR2130327 (2005k:81084)},
}

 




% ----------------------------------------------------- other q chaos

@book {balteshilf,
    AUTHOR = {Baltes, Heinrich P. and Hilf, Eberhard R.},
     TITLE = {Spectra of finite systems},
 PUBLISHER = {Bibliographisches Institut},
   ADDRESS = {Mannheim},
      YEAR = {1976},
     PAGES = {116},
   MRCLASS = {35P20 (69.00)},
  MRNUMBER = {MR0435624 (55 \#8582)},
MRREVIEWER = {A. E. Heins},
}

@article {berry77,
    AUTHOR = {Berry, M. V.},
     TITLE = {Regular and irregular semiclassical wavefunctions},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {10},
      YEAR = {1977},
    NUMBER = {12},
     PAGES = {2083--2091},
    MRCLASS = {81.58 (28A65 58F15)},
  MRNUMBER = {MR0489542 (58 \#8961)},
}

@ARTICLE{austin,
   author = {{Austin}, E.~J. and {Wilkinson}, M.},
    title = "{Distribution of matrix elements of a classically chaotic system}",
  journal = epl,
     year = 1992,
    month = dec,
   volume = 20,
    pages = {589},
  adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System}
}

@article {baeckerbb,
    AUTHOR = {B{\"a}cker, A. and Schubert, R. and Stifter, P.},
     TITLE = {On the number of bouncing ball modes in billiards},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {30},
      YEAR = {1997},
    NUMBER = {19},
     PAGES = {6783--6795},
        CODEN = {JPHAC5},
   MRCLASS = {81Q50},
  MRNUMBER = {MR1481345},
}


@incollection {RMT,
    AUTHOR = {Bohigas, Oriol},
     TITLE = {Random matrix theories and chaotic dynamics},
 BOOKTITLE = {Chaos et physique quantique (Les Houches, 1989)},
     PAGES = {87--199},
 PUBLISHER = {North-Holland},
   ADDRESS = {Amsterdam},
      YEAR = {1991},
   MRCLASS = {82B41 (15A52 58F13 81Q10 81Q50)},
  MRNUMBER = {MR1188418 (94f:82038)},
MRREVIEWER = {Pierre Moussa},
}

@article {casati,
    AUTHOR = {Casati, Giulio and Prosen, Toma{\u{z}}},
     TITLE = {The quantum mechanics of chaotic billiards},
   JOURNAL = {Phys. D},
  FJOURNAL = {Physica D. Nonlinear Phenomena},
    VOLUME = {131},
      YEAR = {1999},
    NUMBER = {1-4},
     PAGES = {293--310},
       CODEN = {PDNPDT},
   MRCLASS = {81Q50},
  MRNUMBER = {MR1726941 (2001m:81082)},
}

@article {doronfrc,
    AUTHOR = {Cohen, Doron},
     TITLE = {Chaos and energy spreading for time-dependent {H}amiltonians,
              and the various regimes in the theory of quantum dissipation},
   JOURNAL = {Ann. Physics},
  FJOURNAL = {Annals of Physics},
    VOLUME = {283},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {175--231},
      CODEN = {ADNYA6},
   MRCLASS = {81Q50},
  MRNUMBER = {MR1769920 (2001g:81081)},
MRREVIEWER = {M. Combescure},
}

@article {prosen3d,
    AUTHOR = {Prosen, Toma{\v{z}}},
     TITLE = {Quantization of a generic chaotic {$3$}{D} billiard with
              smooth boundary. {I}. {E}nergy level statistics},
   JOURNAL = {Phys. Lett. A},
  FJOURNAL = {Physics Letters. A},
    VOLUME = {233},
      YEAR = {1997},
    NUMBER = {4-6},
     PAGES = {323--331},
      CODEN = {PYLAAG},
   MRCLASS = {81Q50},
  MRNUMBER = {MR1474466 (99a:81046)},
MRREVIEWER = {Nariyuki Minami},
}

@article {prosen3d2,
    AUTHOR = {Prosen, Toma{\v{z}}},
     TITLE = {Quantization of generic chaotic {$3$}{D} billiard with smooth
              boundary. {II}. {S}tructure of high-lying eigenstates},
   JOURNAL = {Phys. Lett. A},
  FJOURNAL = {Physics Letters. A},
    VOLUME = {233},
      YEAR = {1997},
    NUMBER = {4-6},
     PAGES = {332--342},
      CODEN = {PYLAAG},
   MRCLASS = {81Q50},
  MRNUMBER = {MR1474467 (99a:81047)},
MRREVIEWER = {Nariyuki Minami},
}

@misc{history,
author={F. Steiner},
title={Quantum Chaos},
note={\url{http://arxiv.org/chao-dyn/9402001}},
year={1994}
}

@article {tanner,
    AUTHOR = {Tanner, Gregor},
     TITLE = {How chaotic is the stadium billiard? {A} semiclassical
              analysis},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {30},
      YEAR = {1997},
    NUMBER = {8},
     PAGES = {2863--2888},
      CODEN = {JPHAC5},
   MRCLASS = {81Q50 (81Q20)},
  MRNUMBER = {MR1450353},
}

 @article {scalinguse1,
    AUTHOR = {Veble, Gregor and Robnik, Marko and Liu, Junxian},
     TITLE = {Study of regular and irregular states in generic systems},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {32},
      YEAR = {1999},
    NUMBER = {36},
     PAGES = {6423--6444},
      CODEN = {JPHAC5},
   MRCLASS = {81Q50 (37J99 37N20 81Q20)},
  MRNUMBER = {MR1732841 (2000k:81106)},
MRREVIEWER = {M. Combescure},
}

 @incollection {debievre,
    AUTHOR = {De Bi{\`e}vre, Stephan},
     TITLE = {Quantum chaos: a brief first visit},
 BOOKTITLE = {Second Summer School in Analysis and Mathematical Physics
              (Cuernavaca, 2000)},
    SERIES = {Contemp. Math.},
    VOLUME = {289},
     PAGES = {161--218},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2001},
   MRCLASS = {81Q50 (37D45 37D50 37N20 81-02)},
  MRNUMBER = {MR1864542 (2002k:81074)},
MRREVIEWER = {Gabriel Gustavo Carlo},
}

@article {fulling,
    AUTHOR = {Fulling, S. A. and Kuchment, Peter},
     TITLE = {Coincidence of length spectra does not imply isospectrality},
   JOURNAL = {Inverse Problems},
  FJOURNAL = {Inverse Problems. An International Journal on the Theory and
              Practice of Inverse Problems, Inverse Methods and Computerized
              Inversion of Data},
    VOLUME = {21},
      YEAR = {2005},
    NUMBER = {4},
     PAGES = {1391--1395},
      CODEN = {INPEEY},
   MRCLASS = {58J53 (35J05 35P05)},
  MRNUMBER = {MR2158116 (2006e:58049)},
MRREVIEWER = {Ruth Gornet},
}

@article {balian,
    AUTHOR = {Balian, R. and Bloch, C.},
     TITLE = {Distribution of eigenfrequencies for the wave equation in a
              finite domain. {I}. {T}hree-dimensional problem with smooth
              boundary surface},
   JOURNAL = {Ann. Physics},
  FJOURNAL = {Annals of Physics},
    VOLUME = {60},
      YEAR = {1970},
     PAGES = {401--447},
    MRCLASS = {35.80},
  MRNUMBER = {MR0270008 (42 \#4901)},
MRREVIEWER = {C. Clark},
}

@article{BRdist,
author={Berry, M. V. and Robnik, M.},
title="Semiclassical level spacings when regular and chaotic orbits coexist",
journal=jpa,
year=1984,
volume=17,
pages={2413--21}
}




% ----------------------------------------- Dynamical tunneling

@article{hacken98,
author={Hackenbroich, Gregor and N\"{o}ckel, Jens U.},
title="Dynamical tunneling in optical cavities",
journal=epl,
volume=39,
pages={371--376},
year=1997
}

@article{fris98,
author="Frischat, S. D.  and Doron, Eyal",
title="Dynamical tunneling in mixed systems",
journal=pre,
volume=57,
pages={1421--43},
year=1998
}

@article{davis81,
author={Davis, M. J. and Heller, E. J.},
title="Quantum dynamical tunneling in bound states",
journal={J. Chem. Phys.},
year=1981,
volume=75,
issue=1,
pages={246--254}
}

@article{loeck07,
author={B\"{a}cker, A. and Ketzmerick, R. and L\"{o}ck, S. and Schilling, L.},
title="Regular-to-chaotic tunneling rates using a fictitious integrable system",
journal="preprint",
note="{\tt arXiv:0707.0217 [nlin.CD]}",
year=2007
}






% ------------------------------------------- physical realizations

@Article{katine,
  title = {Point Contact Conductance of an Open Resonator},
  author = {Katine, J. A. and Eriksson, M. A. and Adourian, A. S. and Westervelt, R. M. and Edwards, J. D. and Lupu-Sax, A.  and Heller, E. J. and Campman, K. L. and Gossard, A. C.},
  journal = {Phys. Rev. Lett.},
  volume = {79},
  number = {24},
  pages = {4806--4809},
  numpages = {3},
  year = {1997},
  month = {Dec},
  doi = {10.1103/PhysRevLett.79.4806},
  publisher = {American Physical Society}
}

@mastersthesis{vidmar,
title="Energy Levels in Microwave Billiards",
author="Gregor Vidmar",
year=2005,
school="Ljubljana, Slovenia",
note="available at
\url{http://www-f9.ijs.si/~krizan/sola/sempod/0405/vidmar.pdf}"
}

@article{sridhar,
    AUTHOR = {Dhar, Abhishek and Madhusudhana Rao, D. and Shankar N.,
              Udaya and Sridhar, S.},
     TITLE = {Isospectrality in chaotic billiards},
   JOURNAL = {Phys. Rev. E (3)},
  FJOURNAL = {Physical Review E. Statistical, Nonlinear, and Soft Matter
              Physics},
    VOLUME = {68},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {026208, 5},
      CODEN = {PLEEE8},
   MRCLASS = {81Q50 (82C05)},
  MRNUMBER = {MR2010079 (2004h:81105)},
}


@article{dietz,
author={Dietz, B. and Friedrich, T. and Miski-Oglu, M. and Richter, A. and
Sch\"{a}fer, S.},
title="Spectral properties of Bunimovich mushroom billiards",
journal=pre,
volume=75,
pages=035203,
year=2007
}

@book{jackson,
author="Jackson, J. D.",
title="Classical Electrodynamics",
edition="3rd",
year=1998,
publisher="Wiley"
}

% -----------------------------------------------other eigenmode properties

@article {hasselltao,
    AUTHOR = {Hassell, Andrew and Tao, Terence},
     TITLE = {Upper and lower bounds for normal derivatives of {D}irichlet
              eigenfunctions},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {9},
      YEAR = {2002},
    NUMBER = {2-3},
     PAGES = {289--305},
      ISSN = {1073-2780},
   MRCLASS = {58J50 (35P15)},
  MRNUMBER = {MR1909646 (2003k:58047)},
MRREVIEWER = {E. Lami Dozo},
}

@article{gerard93,
author={G\'{e}rard, P. and Leichtnam, E.},
title="Ergodic properties of eigenfunctions for the {D}irichlet problem",
journal="Duke Math. J.",
year=1993,
volume=71,
issue=2,
pages={559--607}
}

@article {friedlander,
    AUTHOR = {Friedlander, Leonid},
     TITLE = {Some inequalities between {D}irichlet and {N}eumann
              eigenvalues},
   JOURNAL = {Arch. Rational Mech. Anal.},
  FJOURNAL = {Archive for Rational Mechanics and Analysis},
    VOLUME = {116},
      YEAR = {1991},
    NUMBER = {2},
     PAGES = {153--160},
      ISSN = {0003-9527},
     CODEN = {AVRMAW},
   MRCLASS = {35P15 (47F05 58G25)},
  MRNUMBER = {MR1143438 (93h:35146)},
}

@article {nachman,
    AUTHOR = {Nachman, Adrian and Sylvester, John and Uhlmann, Gunther},
     TITLE = {An {$n$}-dimensional {B}org-{L}evinson theorem},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {115},
      YEAR = {1988},
    NUMBER = {4},
     PAGES = {595--605},
      ISSN = {0010-3616},
     CODEN = {CMPHAY},
   MRCLASS = {35P05 (34B25 35J10 35P25 81C10)},
  MRNUMBER = {MR933457 (89g:35082)},
MRREVIEWER = {Rainer Hempel},
}

@article{netrusov,
author="Yu. Netrusov and Yu. Safarov",
journal=commun,
year=2005,
title="Weyl Asymptotic Formula for the {L}aplacian on Domains
with Rough Boundaries",
volume=253,
pages={481--509}
}

@article{hillairetjudge,
author="L Hillairet and C Judge",
journal="Proc. Amer. Math. Soc.",
title="GENERIC SPECTRAL SIMPLICITY OF POLYGONS",
volume=137,
number=6,
pages={2139--2145},
year=2009
}

% -----------------------------------------------------eigenmode applications

@inbook{tref06,
 AUTHOR = {Trefethen, Lloyd N. and Betcke, Timo},
     TITLE = {Computed eigenmodes of planar regions},
 BOOKTITLE = {Recent advances in differential equations and mathematical
              physics},
    SERIES = {Contemp. Math.},
    VOLUME = {412},
     PAGES = {297--314},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2006}
}

@article{saito,
author="Saito, N.",
title="Data analysis and representation on a general domain using eigenfunctions of {L}aplacian", 
journal="Applied and Computational Harmonic Analysis",
volume="25",
issue=1,
pages={68--97},
year=2008
}

@article{hakan05,
author="Tureci, H. E. and Schwefel, H. G. L. and Jacquod, P. and Stone, A. D.",
title="Modes of wave-chaotic dielectric resonators",
journal="Progress in Optics",
volume="47",
pages="75--137",
year=2005,
}

@Article{narim99,
  title = {Semiclassical Theory of the Emission Properties of Wave-Chaotic Resonant Cavities},
  author = {Narimanov, Evgenii E. and Hackenbroich, Gregor  and Jacquod, Philippe  and Stone, A. Douglas},
  journal = {Phys. Rev. Lett.},
  volume = {83},
  number = {24},
  pages = {4991--4994},
  numpages = {3},
  year = {1999},
  month = {Dec},
  doi = {10.1103/PhysRevLett.83.4991},
  publisher = {American Physical Society}
}

@article{gmachl,
title="High-power directional emission from microlasers with chaotic
resonators",
author="Gmachl, C. and Capasso, F. and Narimanov, E. E. and Nockel, J. U. and Stone, A. D> and Faist, J. and Sivco, D. L. and Cho, A. Y.",
journal="Science",
year=1998,
volume=280,
issue=5369,
pages={1556--1564}
}

@article{kriegs,
author="Kriegsmann, G. A.",
title="Scattering by large resonant cavity structures",
journal="Wave Motion",
year=1999,
volume=30,
pages={329--344}
}

% is some lame numerical eigenmode method, but contains apps to cabins
% and noise levels.
@article{acoustic1,
author="Missaoui, J. and Cheng, L.",
title="A combined integro-modal approach for predicting
acoustic properties of irregular-shaped cavities",
journal="J. Acoust. Soc. Am.",
year=1997,
volume=101,
pages={3313--3321}
}


@book{qdots,
author="Nakamura, K. and Harayama, T.",
title="Quantum Chaos and Quantum Dots",
year=2004,
publisher="Oxford Univ. Press"
}

% gravity atom billiards:....
@article{milner01,
author="Milner, V. and Hanssen, J. L. and Campbell, W. C. and Raizen, M. G.",
year=2001,
title="Optical billiards for atoms",
journal=prl,
volume=86,
pages={1514--1519}
}




% --------------------------------------------------- isospectral

@article {gww,
    AUTHOR = {Gordon, C. and Webb, D. and Wolpert, S.},
     TITLE = {Isospectral plane domains and surfaces via {R}iemannian
              orbifolds},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {110},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {1--22},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {58G99},
  MRNUMBER = {MR1181812 (93h:58172)},
MRREVIEWER = {Robert Brooks},
}

@article {driscoll,
    AUTHOR = {Driscoll, Tobin A.},
     TITLE = {Eigenmodes of isospectral drums},
   JOURNAL = {SIAM Rev.},
  FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and
              Applied Mathematics},
    VOLUME = {39},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {1--17},
      ISSN = {0036-1445},
     CODEN = {SIREAD},
   MRCLASS = {65N25 (35P99)},
  MRNUMBER = {MR1439483 (97m:65198)},
MRREVIEWER = {J. T. Oden},
}

@Article{dris03,
  title = {Isospectral shapes with Neumann and alternating boundary conditions},
  author = {Driscoll, T. A. and Gottlieb, H. P. W.},
  journal = {Phys. Rev. E},
  volume = {68},
  number = {1},
  pages = {016702},
  numpages = {6},
  year = {2003},
  month = {Jul},
  doi = {10.1103/PhysRevE.68.016702},
  publisher = {American Physical Society}
}

@article{GiraudThas,
author={O Giraud and K Thas},
title="Hearing shapes of drums: Mathematical and physical aspects of isospectrality",
journal={Rev.\ Mod.\ Phys.},
year=2010,
volume=82,
pages={2213--2255}
}

% ------------------------------------------eigenmode numerical methods 


@article {fhm,
    AUTHOR = {Fox, L. and Henrici, P. and Moler, C.},
     TITLE = {Approximations and bounds for eigenvalues of elliptic
              operators},
   JOURNAL = {SIAM J. Numer. Anal.},
  FJOURNAL = {SIAM Journal on Numerical Analysis},
    VOLUME = {4},
      YEAR = {1967},
     PAGES = {89--102},
    MRCLASS = {65.66},
  MRNUMBER = {MR0215542 (35 \#6382)},
MRREVIEWER = {L. Collatz},
}

 
@article {molerpayne,
    AUTHOR = {Moler, C. B. and Payne, L. E.},
     TITLE = {Bounds for eigenvalues and eigenvectors of symmetric
              operators},
   JOURNAL = {SIAM J. Numer. Anal.},
  FJOURNAL = {SIAM Journal on Numerical Analysis},
    VOLUME = {5},
      YEAR = {1968},
     PAGES = {64--70}
}
%    MRCLASS = {65.35},
%  MRNUMBER = {MR0226833 (37 \#2420)},
%MRREVIEWER = {James H. Wilkinson},

@article {descloux,
    AUTHOR = {Descloux, J. and Tolley, M.},
     TITLE = {An accurate algorithm for computing the eigenvalues of a
              polygonal membrane},
   JOURNAL = {Comput. Methods Appl. Mech. Engrg.},
  FJOURNAL = {Computer Methods in Applied Mechanics and Engineering},
    VOLUME = {39},
      YEAR = {1983},
    NUMBER = {1},
     PAGES = {37--53},
      ISSN = {0045-7825},
     CODEN = {CMMECC},
   MRCLASS = {73K15 (65N25)},
  MRNUMBER = {MR712205 (84i:73056)},
}

@article{still,
author="Still, G.",
title="Computable bounds for eigenvalues and eigenfunctions of elliptic
differential operators",
journal="Numer. Math.",
year=1988,
volume=54,
pages={201--223}
}

@article {mps,
    AUTHOR = {Betcke, Timo and Trefethen, Lloyd N.},
     TITLE = {Reviving the method of particular solutions},
   JOURNAL = {SIAM Rev.},
  FJOURNAL = {SIAM Review},
    VOLUME = {47},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {469--491}
}
%    MRCLASS = {65N25},
%  MRNUMBER = {MR2178637},

@phdthesis{timothesis,
author="Betcke, T.",
title="Computations of Eigenfunctions of Planar Regions",
school="Oxford University, UK",
year=2005
}


@article{gsvd,
author="Betcke, T.",
title = "The generalized singular value decomposition and the {M}ethod of {P}articular {S}olutions",
journal = "SIAM J. Sci. Comp.",
year = {2008},
volume=30,
pages={1278--1295}
}

@article{timodd,
author={Betcke, T.},
title="A {GSVD} formulation of a domain decomposition method for planar eigenvalue problems",
journal="IMA J. Numer. Anal.",
volume="27",
pages="451--478",
year=2007
}

@incollection {backerbim,
    AUTHOR = {B{\"a}cker, Arnd},
     TITLE = {Numerical aspects of eigenvalue and eigenfunction computations
              for chaotic quantum systems},
 BOOKTITLE = {The mathematical aspects of quantum maps},
    SERIES = {Lecture Notes in Phys.},
    VOLUME = {618},
     PAGES = {91--144},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2003},
   MRCLASS = {65F15 (81-04 81Q50)},
  MRNUMBER = {MR2159324},
}

@article{kosztin,
author={Ioan Kosztin and Klaus Schulten},
title={Boundary Integral Method for Stationary States of Two-Dimensional Quantum Systems},
journal={Internat. J. Modern Phys. C},
volume={8},
number=2,
pages={293--325},
year=1997
} 

@article {KS,
    AUTHOR = {Kuttler, J. R. and Sigillito, V. G.},
     TITLE = {Eigenvalues of the {L}aplacian in two dimensions},
   JOURNAL = {SIAM Rev.},
  FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and
              Applied Mathematics},
    VOLUME = {26},
      YEAR = {1984},
    NUMBER = {2},
     PAGES = {163--193},
      CODEN = {SIREAD},
   MRCLASS = {65N25 (35J05 35P05 76Q05 78A50)},
  MRNUMBER = {MR738929 (85k:65086)},
MRREVIEWER = {P. Keast},
}

% also known as Ku78
@article {KSbounds,
    AUTHOR = {Kuttler, J. R. and Sigillito, V. G.},
     TITLE = {Bounding eigenvalues of elliptic operators},
   JOURNAL = {SIAM J. Math. Anal.},
  FJOURNAL = {SIAM Journal on Mathematical Analysis},
    VOLUME = {9},
      YEAR = {1978},
    NUMBER = {4},
     PAGES = {768--778},
    MRCLASS = {35P15 (49G05)},
  MRNUMBER = {MR0492948 (58 \#11996)},
MRREVIEWER = {L. E. Payne},
}

@article{v+s,
  author = {E. Vergini and M. Saraceno},
  title = {Calculation by scaling of highly excited states of billiards},
  year = 1995,
  journal = pre,
  volume = "52",
number={3},
  pages = {2204--2207}
}

@phdthesis{verginithesis,
  author = {E. Vergini},
  title = {Estudio Cu\'{a}ntico y Semicl\'{a}sico de Billares Cl\'{a}sicamente
Ca\'{o}ticos},
  year = 1995,
  school = {Universidad de Buenos Aires}
}


% unfinished.... got from Timo:
@article{eisencluster,
author="Eisenstat, S. C.",
title="Bounds for eigenvalues and eigenvectors of self-adjoint operators",
note="{\em preprint}",
year=2006
}


@article{riddell,
title="Numerical solution of the {H}elmholtz equation for two-dimensional polygonal regions",
author="Riddell, R. J",
journal=jcp,
year=1979,
volume=31,
pages={42--59}
}

@article {KSstek,
    AUTHOR = {Kuttler, J. R. and Sigillito, V. G.},
     TITLE = {Inequalities for membrane and {S}tekloff eigenvalues},
   JOURNAL = {J. Math. Anal. Appl.},
  FJOURNAL = {Journal of Mathematical Analysis and Applications},
    VOLUME = {23},
      YEAR = {1968},
     PAGES = {148--160},
      ISSN = {0022-247x},
   MRCLASS = {35.80},
  MRNUMBER = {MR0226226 (37 \#1816)},
MRREVIEWER = {L. E. Payne},
}

@article{ferrero,
author="Ferrero, A. and Gazzola, F. and Weth, T.",
title="On a fourth order {S}teklov eigenvalue problem",
journal="Analysis",
volume=25,
pages={315--332},
year=2005
}

@article{bucur,
author="Dorin Bucur and Alberto Ferrero and Filippo Gazzola",
title="On the first eigenvalue of a fourth order {S}teklov problem",
year=2009,
journal="Calc. Var.",
volume=35,
pages={103--131}
}

@article{chenhua,
author="Hua Chen",
journal="Acta Math. Sinica, New Series",
year=1995,
title="Irregular but non-fractal drums, and $n$-dimensional {W}eyl conjecture",
volume=11,
number=2,
pages={168--178}
}

@article{litrefftz,
author={Li, Z. C.},
journal={Applied Numer. Math.},
title="The {T}refftz method for the {H}elmholtz equation with degeneracy",
year=2008,
volume=58,
pages={131--159}
}

@article{berrydiab,
author={M V Berry and M Wilkinson},
title={Diabolical points in the spectra of triangles},
year=1984,
journal=proy,
volume=392,
pages={15--43}
}

@article{steinbachunger,
author={O Steinbach and G Unger},
title={A boundary element method for the {D}irichlet eigenvalue problem of the {L}aplace operator},
year=2009,
journal={Numer. Math.},
volume=113,
pages={281--298}
}

@article{duran,
author={M. Dur\'an and J.-C. N\'ed\'elec and S. Ossand\'on},
title={An Efficient {G}alerkin {BEM} to Compute High Acoustic Eigenfrequencies},
journal={J. Vib. Acoust.},
year=2009,
volume=131,
number=3,
pages={03100(1--9)}
}

@article{kirkup,
author={S. M. Kirkup and S. Amini},
title={Solution of the {H}elmholtz Eigenvalue Problem via the Boundary Element Method},
journal={Int. J. Numer. Meth. Eng.},
volume=36,
number=2,
pages={321--330},
year=1993
}

@article{lepore,
author={D Cohen and N Lepore and E J Heller},
title={Consolidating boundary methods for finding the eigenstates of billiards},
journal=jpa,
year=2004,
volume=37,
pages={2139--2161}
}

@article{tai74,
author={G R C Tai and R P Shaw},
title={{H}elmholtz-equation eigenvalues and eigenmodes for arbitrary
domains},
journal={J. Acoust.\ Soc.\ Am.},
year=1974,
volume=56,
number=3,
pages={796--804}
}

@incollection{babosrev,
author={I M Babuska and J Osborn},
title={Eigenvalue problems},
booktitle={Handbook of numerical analysis, Volume {II}},
pages={643--787},
editor={P G Ciarlet and J I Lions},
year=1991,
publisher={Elsevier (North-Holland)}
}


% FEM:
@article{demen07,
title="Numerical experiments on quantum chaotic billiards",
author="de Menezes, D. D. and Jar E. Silva, M. and de Aguiar, F. M.",
journal="CHAOS",
volume=17,
issue=2,
year=2007,
pages="023116"
}

% FEM
@article{dietzFEM,
author={B Dietz and A Heine and V Heuveline and A Richter},
title="Test of a numerical approach to the quantization of billiards",
year=2005,
journal=pre,
volume={71},
pages={026703}
}

% best FEM so far?
@article{heuveline,
author={V Heuveline},
title={On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods},
journal=jcp,
volume=184,
year=2003,
pages={321--337}
}

% scaling variant:
@article{veblemonza,
author={G Veble and T Prosen and M Robnik},
title="Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards",
journal={New J.\ Phys.},
year=2007,
volume=9,
pages=15
}

% scaling variant:
@article{hakansca,
title={An efficient {F}redholm method for calculation of highly excited states of billiards},
author={Hakan E. Tureci and H. G. L. Schwefel},
journal=jpa,
volume=40,
pages=13869,
year=2007
}


% ---------------------------------------------- MFS / fundamental solutions


@article {Smyrl,
    AUTHOR = {Smyrlis, Yiorgos-Sokratis and Karageorghis, Andreas},
     TITLE = {Numerical analysis of the {MFS} for certain harmonic problems},
   JOURNAL = {M2AN Math. Model. Numer. Anal.},
  FJOURNAL = {M2AN. Mathematical Modelling and Numerical Analysis},
    VOLUME = {38},
      YEAR = {2004},
    NUMBER = {3},
     PAGES = {495--517}
}

@article{En96,
    AUTHOR = {Ennenbach, R. and Niemeyer, H.},
     TITLE = {The inclusion of {D}irichlet eigenvalues with singularity
              functions},
   JOURNAL = {Z. Angew. Math. Mech.},
  FJOURNAL = {Zeitschrift f\"ur Angewandte Mathematik und Mechanik},
    VOLUME = {76},
      YEAR = {1996},
    NUMBER = {7},
     PAGES = {377--383}
}

@article {Ka01,
    AUTHOR = {Karageorghis, A.},
     TITLE = {The method of fundamental solutions for the calculation of the
              eigenvalues of the {H}elmholtz equation},
   JOURNAL = {Appl. Math. Lett.},
  FJOURNAL = {Applied Mathematics Letters. An International Journal of Rapid
              Publication},
    VOLUME = {14},
      YEAR = {2001},
    NUMBER = {7},
     PAGES = {837--842},
      ISSN = {0893-9659},
     CODEN = {AMLEEL},
   MRCLASS = {65N25},
  MRNUMBER = {MR1849238 (2002e:65167)},
}



@article {FaKa98,
    AUTHOR = {Fairweather, Graeme and Karageorghis, Andreas},
     TITLE = {The method of fundamental solutions for elliptic boundary
              value problems},
   JOURNAL = {Adv. Comput. Math.},
  FJOURNAL = {Advances in Computational Mathematics},
    VOLUME = {9},
      YEAR = {1998},
    NUMBER = {1-2},
     PAGES = {69--95},
      ISSN = {1019-7168},
   MRCLASS = {65N99},
  MRNUMBER = {MR1662760 (2000a:65165)},
MRREVIEWER = {H. Marcinkowska},
}

@article {Pe06,
    AUTHOR = {Perrey-Debain, E.},
     TITLE = {Plane wave decomposition in the unit disc: convergence
              estimates and computational aspects},
   JOURNAL = {J. Comput. Appl. Math.},
  FJOURNAL = {Journal of Computational and Applied Mathematics},
    VOLUME = {193},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {140--156},
      ISSN = {0377-0427},
     CODEN = {JCAMDI},
   MRCLASS = {35L05 (76M25 78A40)},
  MRNUMBER = {MR2228711 (2006m:35210)},
}

@article {Ka89,
    AUTHOR = {Katsurada, Masashi},
     TITLE = {A mathematical study of the charge simulation method. {II}},
   JOURNAL = {J. Fac. Sci. Univ. Tokyo Sect. IA Math.},
  FJOURNAL = {Journal of the Faculty of Science. University of Tokyo.
              Section IA. Mathematics},
    VOLUME = {36},
      YEAR = {1989},
    NUMBER = {1},
     PAGES = {135--162},
      ISSN = {0040-8980},
     CODEN = {JFTMAT},
   MRCLASS = {35J05 (35J25 65N35 78A30)},
  MRNUMBER = {MR991024 (90d:35061)},
MRREVIEWER = {H. Kersten},
}

@article {Ka88,
    AUTHOR = {Katsurada, Masashi and Okamoto, Hisashi},
     TITLE = {A mathematical study of the charge simulation method. {I}},
   JOURNAL = {J. Fac. Sci. Univ. Tokyo Sect. IA Math.},
  FJOURNAL = {Journal of the Faculty of Science. University of Tokyo.
              Section IA. Mathematics},
    VOLUME = {35},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {507--518},
      ISSN = {0040-8980},
     CODEN = {JFTMAT},
   MRCLASS = {65N35 (35J05)},
  MRNUMBER = {MR965011 (90a:65247)},
MRREVIEWER = {H. Kersten},
}

@article {Ka90,
    AUTHOR = {Katsurada, Masashi},
     TITLE = {Asymptotic error analysis of the charge simulation method in a
              {J}ordan region with an analytic boundary},
   JOURNAL = {J. Fac. Sci. Univ. Tokyo Sect. IA Math.},
  FJOURNAL = {Journal of the Faculty of Science. University of Tokyo.
              Section IA. Mathematics},
    VOLUME = {37},
      YEAR = {1990},
    NUMBER = {3},
     PAGES = {635--657},
      ISSN = {0040-8980},
     CODEN = {JFTMAT},
   MRCLASS = {65N15},
  MRNUMBER = {MR1080874 (91m:65263)},
MRREVIEWER = {J. T. Oden},
}

@article {Ka94,
    AUTHOR = {Katsurada, Masashi},
     TITLE = {Charge simulation method using exterior mapping functions},
   JOURNAL = {Japan J. Indust. Appl. Math.},
  FJOURNAL = {Japan Journal of Industrial and Applied Mathematics},
    VOLUME = {11},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {47--61},
      ISSN = {0916-7005},
   MRCLASS = {65N35 (35E05)},
  MRNUMBER = {MR1266520 (94k:65170)},
}

@article {Ka96,
    AUTHOR = {Katsurada, M. and Okamoto, H.},
     TITLE = {The collocation points of the fundamental solution method for
              the potential problem},
   JOURNAL = {Comput. Math. Appl.},
  FJOURNAL = {Computers \& Mathematics with Applications. An International
              Journal},
    VOLUME = {31},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {123--137},
      ISSN = {0898-1221},
     CODEN = {CMAPDK},
   MRCLASS = {65N35},
  MRNUMBER = {MR1362387},
}

@article {SmKa03,
    AUTHOR = {Smyrlis, Yiorgos-Sokratis and Karageorghis, Andreas},
     TITLE = {Some aspects of the method of fundamental solutions for
              certain biharmonic problems},
   JOURNAL = {CMES Comput. Model. Eng. Sci.},
  FJOURNAL = {CMES. Computer Modeling in Engineering \& Sciences},
    VOLUME = {4},
      YEAR = {2003},
    NUMBER = {5},
     PAGES = {535--550},
      ISSN = {1526-1492},
   MRCLASS = {65N99},
  MRNUMBER = {MR2007249},
}

@article {SmKa01,
    AUTHOR = {Smyrlis, Yiorgos-Sokratis and Karageorghis, Andreas},
     TITLE = {Some aspects of the method of fundamental solutions for
              certain harmonic problems},
   JOURNAL = {J. Sci. Comput.},
  FJOURNAL = {Journal of Scientific Computing},
    VOLUME = {16},
      YEAR = {2001},
    NUMBER = {3},
     PAGES = {341--371},
      ISSN = {0885-7474},
     CODEN = {JSCOEB},
   MRCLASS = {65N35 (65N99)},
  MRNUMBER = {MR1873287 (2002i:65136)},
}

@inproceedings {UsCh03,
    AUTHOR = {Ushijima, Teruo and Chiba, Fumihiro},
     TITLE = {A fundamental solution method for the reduced wave problem in
              a domain exterior to a disc},
 BOOKTITLE = {Proceedings of the International Conference on Recent Advances
              in Computational Mathematics (ICRACM 2001) (Matsuyama)},
   JOURNAL = {J. Comput. Appl. Math.},
  FJOURNAL = {Journal of Computational and Applied Mathematics},
    VOLUME = {152},
      YEAR = {2003},
    NUMBER = {1-2},
     PAGES = {545--557},
      ISSN = {0377-0427},
     CODEN = {JCAMDI},
   MRCLASS = {65N35 (35J05 35J25)},
  MRNUMBER = {MR1991315 (2004f:65200)},
}

@article{Bo85,
author = {Alexander Bogomolny},
collaboration = {},
title = {Fundamental Solutions Method for Elliptic Boundary Value Problems},
publisher = {SIAM},
year = {1985},
journal = {SIAM Journal on Numerical Analysis},
volume = {22},
number = {4},
pages = {644-669},
doi = {10.1137/0722040}
}

@inproceedings {Ki91,
    AUTHOR = {Kitagawa, Takashi},
     TITLE = {Asymptotic stability of the fundamental solution method},
 BOOKTITLE = {Proceedings of the International Symposium on Computational
              Mathematics (Matsuyama, 1990)},
   JOURNAL = {J. Comput. Appl. Math.},
  FJOURNAL = {Journal of Computational and Applied Mathematics},
    VOLUME = 38,
      YEAR = 1991,
     PAGES = {263--269},
      ISSN = {0377-0427},
     CODEN = {JCAMDI},
   MRCLASS = {65N12 (65N35)},
  MRNUMBER = {MR1146984},
}

@article {Ki88,
    AUTHOR = {Kitagawa, Takashi},
     TITLE = {On the numerical stability of the method of fundamental
              solution applied to the {D}irichlet problem},
   JOURNAL = {Japan J. Appl. Math.},
  FJOURNAL = {Japan Journal of Applied Mathematics},
    VOLUME = {5},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {123--133},
      ISSN = {0910-2043},
   MRCLASS = {65N10},
  MRNUMBER = {MR924746 (89a:65152)},
MRREVIEWER = {M. K. Kadalbajoo},
}

@ARTICLE{Ky96,
  AUTHOR =       {Kyurkchan, A. G. and Sternin, B. Yu and Shatalov, V. E.},
  TITLE =        {Singularities of continuation of wave fields},
  JOURNAL =      {Physics - Uspekhi},
  YEAR =         {1996},
  volume =       {12},
  pages =        {1221--1242},
}

@article {Ky85,
    AUTHOR = {Kyurkchan, A. G.},
     TITLE = {The method of auxiliary currents and sources in wave
              diffraction problems},
   JOURNAL = {Soviet J. Comm. Tech. Electron.},
    VOLUME = 30,
      YEAR = 1985,
     PAGES = {48--58},
     NOTE  = {translated from Radiotekhn. i \`Elektron. 29 (1984), no. 11, 2129--2139 (Russian)},
}

@inproceedings {Kark01,
author="Karkashadze, D.",
title="On status of main singularities in {3D} scattering problems",
booktitle = {Proceedings of VIth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED)},
address = {Lviv, Ukraine},
year=2001,
pages={187--190}
}

@book{doicu,
author="Doicu, A. and Eremin, Y. A. and Wriedt, T.",
title="Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources",
year=2000,
address="San Diego, CA",
publisher="Academic Press"
}


@article{gottlieb,
author="Gottlieb, B. and Kleber, M. and Krause, J.",
title="Tunneling from a 3-Dimensional quantum well in an electric field: an analytical solution",
journal="Z. Phys. A",
volume=339,
year=1991,
pages={201--206}
}

@article{bracher,
author="Bracher, C. and Becker, W. and Gurvitz, S. A. and
Kleber, M. and Marinov, M. S.",
title="Three-dimensional tunneling in quantum ballistic motion",
year=1998,
journal="Am. J. Phys.",
volume=66,
issue=1,
pages={38--48}
}

@article{hochman,
author="Hochman, A. and Leviatan, Y.",
title="Efficient and spurious-free
integral-equation-based optical waveguide mode solver",
journal=oe,
year=2007,
volume=15,
issue=22,
pages={14431--53}
}

@article{Ahmed89,
author="Ahmed, M. T. and Lavers, J. D. and Burke, B. E.",
title="An evaluateion of the direct boundary element method and the
method of fundamental solutions",
journal="IEEE Trans. Magn.",
year=1989,
volume=25,
issue=4,
pages={3001--6}
}

@article{ganesh10,
title="A far-field based {T}-matrix method for two dimensional obstacle
scattering",
author={M. Ganesh and S. C. Hawkins},
journal={ANZIAM J.},
volume={51},
year=2010,
pages={215--230}
}


% ------------------------------------------ wave scattering

@article{brunoFMM,
author="Bruno, O. P. and Kunyansky, L. A.",
title="A fast, high-order algorithm for the solution of surface scattering problems:
basic implementation, tests, and applications",
journal=jcp,
year=2001,
volume=169,
pages={80--110}
}

@article{bruno01,
author="Bruno, O. P. and Kunyansky, L. A.",
title="Surface scattering in three dimensions: ",
journal="Proc. R. Soc. Lond. A",
year=2001,
volume=457,
pages={2921--2934}
}

@article{monkwang,
author="Monk, P. and Wang, D.-Q.",
title="A least-squares method for the {H}elmholtz equation",
journal="Comput. Meth. Appl. Mech. Engrg.",
year=1999,
volume=175,
pages={121--136}
}

@article{uwvf,
title={Application of an Ultra Weak Variational Formulation of Elliptic {PDE}S to the Two-Dimensional {H}elmholtz Problem},
author={Olivier Cessenat and Bruno Despres},
journal=sinum,
volume=35,
number=1,
year=1998,
pages={255--299}
}

@article{zickar,
author="Zickar, M. and Noell, W. and Marxer, C. and de Rooij, N.",
year=2006,
title="{MEMS} compatible micro-{GRIN} lenses for fiber to chip coupling of light",
journal=oe,
volume=14,
issue=10,
pages={4237--49}
}

@article{langdon,
author="Chandler-Wilde, S. N. and Langdon, S.",
title="A Galerkin boundary element method for high frequency
scattering by convex polygons",
year=2007,
journal="SIAM J. Num. Anal.",
volume=43,
pages={610--640}
}

@article{Mart05,
author="Martinsson, P. G. and Rokhlin, V.",
title="A fast direct solver for boundary integral equations in two dimensions",
journal=jcp,
year=2005,
volume=205,
pages={1--23}
}

@misc{youngmart,
author={P. Young and P.G. Martinsson},
title={A high order {N}ystr\"om method for boundary integral equations on axisymmetric surfaces},
note={preprint, {\tt arXiv.org:1002.2001}},
year=2010
}

@article{ying06,
author={L Ying and G Biros and D Zorin},
title={A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains},
year=2006,
journal=jcp,
volume=216,
pages={247--275}
}

@article{kirsch,
author={A. Kirsch and P. Monk},
title={An analysis of the coupling of finite-element and {N}ystr\"{o}m
methods in acoustic scattering},
journal={IMA J. Numer. Anal.},
volume=14,
year=1994,
pages={523--544}
}

@article{CWrealline,
title={Boundary integral equations on unbounded rough surfaces: {F}redholmness and the finite section method},
author={S N Chandler-Wilde and M Lindner},
year=2008,
journal={J. Integral Equations Appl.},
volume=20,
pages={13--48}
}

@misc{zydtri,
author={Zydrunas Gimbutas and Leslie Greengard},
title={A simple implementation of the {FMM} for time-harmonic scattering problems},
note="in preparation",
year=2010
}

@misc{HFMM2D,
author={Zydrunas Gimbutas and Leslie Greengard},
title={{HFMM2D}, {F}ortran code for fast multipole method with {H}elmholtz kernel in two dimensions (version 20110313)},
year=2011,
note={{\tt http://www.cims.nyu.edu/cmcl/fmm2dlib/fmm2dlib.html}}
}


@article{ainsworth,
journal=sinum,
author="M Ainsworth",
volume=42,
pages={553--575},
title="Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number",
year=2004
}

@article{pollution,
journal=sinum,
author={I M Babuska and S A Sauter},
title={Is the pollution effect of the {FEM} avoidable for the {H}elmholtz equation considering high wave numbers?},
year=1997,
volume=34,
number=6,
pages={2392--2423}
}

% ----------------------------------------- Computational E&M

@book{CMS,
   author = {W. C. Chew and J. M. Jin and E. Michielssen and J. Song},
   title = {Fast and Efficient Algorithms in Computational Electromagnetics},
   publisher = {Artech House, Boston, MA},
   year = {2001}
}

@book{hafner90,
author="Hafner, C.",
title="The Generalized Multipole Technique for Computational Electromagnetics",
publisher="Artech House Books",
address="Boston",
year=1990
}

@book{muller,
author="C M{\"{u}}ller",
title="Foundations of the Mathematical Theory of Electromagnetic Waves",
publisher="Springer-Verlag, Berlin, New York",
year=1969
}

@book{taflove,
author={A. Taflove},
title={Computational Electrodynamics: The Finite-Difference Time-Domain Method},
publisher={Artech House, Norwood, MA},
year={1995}
}

@misc{epgreenoneil,
author={C L Epstein and L Greengard and M O'Neil},
title={{D}ebye Sources and the Numerical Solution of the Time Harmonic {M}axwell Equations, II},
note={preprint, {\tt arXiv:1105.3217}},
year=2011
}

@book{chewbook,
author={Weng Cho Chew},
title={Waves and Fields in Inhomogeneous Media},
year=1999,
publisher={Wiley-IEEE Press}
}
%(IEEE Press Series on Electromagnetic Wave Theory)}


% ------------------------------ solar cells & absorbers

@article{saeta,
title="How much can guided modes enhance
absorption in thin solar cells?",
author="Peter N. Saeta and Vivian E. Ferry and Domenico Pacifici and Jeremy N. Munday and Harry A. Atwater",
journal=oe,
volume=17,
number=23,
year=2009,
pages={20975--20990}
}

@article{atwater,
title={Plasmonics for improved photovoltaic devices},
pages={205--213},
author={Harry A. Atwater and Albert Polman},
year=2010,
journal={Nature Materials},
volume=9,
number=3
}

@misc{atwaterreport,
title={Plasmonic photovoltaics},
author={H. A. Atwater and K. Langeland and I. Price and V. Ferry},
note={GCEP Progress Report April 30th, 2010},
}


@article{kelzenberg,
title={Enhanced absorption and carrier collection in {S}i
wire arrays for photovoltaic applications},
author={Michael D. Kelzenberg and Shannon W. Boettcher and Jan A. Petykiewicz and Daniel B. Turner-Evans and
Morgan C. Putnam and Emily L. Warren and Joshua M. Spurgeon and Ryan M. Briggs and Nathan S. Lewis
and Harry A. Atwater},
journal={Nature Materials},
year=2010,
volume=9,
number=3,
pages={239--244}
}

@article{absorber,
title={High performance solar-selective absorbers
using coated sub-wavelength gratings},
author={Nicholas P. Sergeant and Mukul Agrawal and Peter Peumans},
journal=oe,
year=2010,
volume=18,
number=6,
pages={5525--5540}
}

% ------------------------- Periodic Problems,  Lattice Sums, Photonic Crystals

@article{berman,
author="Berman, C. L. and Greengard, L.",
title="A renormalization method for the evaluation of lattice sums",
journal=jmp,
year=1994,
volume=35,
issue=11,
pages={6036--6048}
}

@article{Chin94,
  title = {{G}reen's function and lattice sums for electromagnetic scattering by a square array of cylinders},
  author = {Chin, S. K. and Nicorovici, N. A. and McPhedran, R. C.},
  journal = {Phys. Rev. E},
  volume = {49},
  number = {5},
  pages = {4590--4602},
  numpages = {12},
  year = {1994},
  month = {May},
  doi = {10.1103/PhysRevE.49.4590},
  publisher = {American Physical Society}
}

@article{McPh00,
author="{McPhedran}, R. C. and Nicorovici, N. A. and Botten, L. C. and
Grubits, K. A.",
title="Lattice sums for gratings and arrays",
journal=jmp,
volume=41,
issue=11,
year=2000,
pages={7808--7816}
}

@article{Moroz01,
author="Moroz, A.",
title="Exponentially convergent lattice sums",
journal="Opt. Lett.",
year=2001,
volume=26,
issue=15,
pages={1119--21}
}

@article{dienst01,
year=2001,
author="Dienstfrey, A. and Hang, F. and Huang, J.",
title={Lattice sums and the two-dimensional, periodic
{G}reen's function for the {H}elmholtz equation},
journal="Proc. R. Soc. Lond. A",
volume=457,
pages={67--85}
}

@Article{leung93,
  title = {Multiple-scattering calculation of the two-dimensional photonic band structure},
  author = {Leung, K. M. and Qiu, Y. },
  journal = {Phys. Rev. B},
  volume = {48},
  number = {11},
  pages = {7767--7771},
  numpages = {4},
  year = {1993},
  month = {Sep},
  doi = {10.1103/PhysRevB.48.7767},
  publisher = {American Physical Society}
}

@article{linton07,
title="Resonant effects in scattering by periodic arrays",
author="Linton, C. M. and Thompson, I.",
year=2007,
journal="Wave Motion",
volume=44,
pages={165--175}
}

@article{peter06,
title="Water-wave scattering by a periodic arrya of arbitrary bodies",
author={Peter, Malte A. and Meylan, Michael H. and Linton, C. M.},
year=2006,
journal="J. Fluid Mech.",
volume=548,
pages={237--256}
}

@article{linton98,
author="Linton, C. M.",
title="The {G}reen's function for the two-dimensional {H}elmholtz equation in periodic domains",
journal="J. Eng. Math.",
volume=33,
pages={377--402},
year=1998
}

@article{lintonrev,
author={Linton, C. M.},
title={Lattice sums for the {H}elmholtz equation},
journal=sirev,
volume=52,
number=4,
pages={603--674},
year=2010
}
%DOI is 10.1137/09075130X
%howpublished={available at {\tt http://www.lboro.ac.uk/departments/ma/research/preprints/papers09/09-04.pdf}},


@misc{arens10,
title={Analysing {E}wald's Method for the Evaluation of {G}reen's Functions for Periodic Media},
author={T Arens and K Sandfort and Suzanne Schmitt and A Lechleiter},
note="Preprint, submitted to IMA J. Numer. Anal.",
year=2010
}
% available at {\tt http://digbib.ubka.uni-karlsruhe.de/volltexte/1000019136}",

@article{wood,
author="R W Wood",
title="On a remarkable case of uneven distribution of light in a diffraction grating spectrum",
journal={Philos. Mag.},
volume=4,
year=1902,
pages={396­-408}
}

@article{smajic,
author="Smajic, J. and Hafner, C. and Erni, D.",
title="Automatic Calculation of band diagrams of photonic crystals using
the {M}ultiple {M}ultipole {M}ethod",
journal="Appl. Comput. Electromag. Soc. J.",
year=2003,
issue=3,
volume=18,
pages={172--180}
}

@book{jobook,
author="Joannopoulos, J. D. and Johnson, S. G. and Meade, R. D. and Winn, J. N.",
year=2008,
title="Photonic Crystals: Molding the Flow of Light",
publisher="Princeton Univ. Press",
address="Princeton, NJ",
edition="2nd"
}

@article{yuan08,
author="Yuan, J. and Lu, Y. Y. and Antoine, X.",
year=2008,
journal=jcp,
title="Modeling photonic crystals by boundary integral equations and {Dirichlet-to-Neumann} maps",
volume=227,
pages="4617--4629"
}

@article{rokh83,
author="Rokhlin, V.",
journal="Wave Motion",
year=1983,
title="Solution of acoustic scattering problems by means of second kind integral equations",
volume=5,
pages={257--272}
}

@article{otani08,
author="Otani, Y. and Nishimura, N.",
title="A periodic {FMM} for {M}axwell's equations in {3D} and
its applications to problems related to photonic crystals",
journal=jcp,
year=2008,
volume=227,
pages={4630--52}
}

@article{fmm1,
author="Cheng, H. and Crutchfield, W. Y. and  Gimbutas, Z. and Greengard L.
and  Ethridge,  F. and  Huang , J. and Rokhlin , V. and  Yarvin, N. and Zhao, J.",
title="A Wideband Fast Multipole Method for the {H}elmholtz Equation
   in Three Dimensions",
journal="J. Comput. Phys.",
volume=216,
year=2006,
pages={300--325}
}


@inbook{fmm2,
author="Cheng, H. and Crutchfield, W. Y. and  Gimbutas, Z. and Greengard L. 
and  Huang , J. and Rokhlin , V. and  Yarvin, N. and Zhao, J.",
title={Remarks on the implementation of the wideband FMM for the Helmholtz 
   equation in two dimensions},
 booktitle = {Inverse Problems, Multi-Scale Analysis and Effective Medium Theory},
    SERIES = {Contemp. Math.},
    VOLUME = {408},
     PAGES = {99--110},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2006}
}

@article{fmmlattice,
author="Berman, C. L. and Greengard, L.", 
title="A Renormalization Method for the Evaluation of Lattice Sums",
journal="J. Math. Phys.",
volume=35,
year=1994,
pages={6036--6048}
}

@article{kress91,
author="Kress, R.",
title="Boundary Integral   equations in time-harmonic acoustic scattering",
journal="Mathl. Comput. Modelling",
volume=15,
issue={3--5},
year=1991,
pages={229--243}
}

@article{nystrom,
author={Nystr{\"o}m, E.J.},
title={{\"U}ber die praktische {Aufl\"osung} von {Integralgleichungen} mit {Andwendungen} aug {Randwertaufgaben}},
journal={Acta Math.},
volume=54,
pages={185--204},
year=1930
}

@incollection{kressacrev,
author="Kress, R.",
title="Acoustic scattering: {S}pecific theoretical tools (topic 1.2.1) and {S}cattering by obstacles (topic 1.2.2)",
booktitle="Scattering: Scattering and Inverse Scattering in Pure and Applied Science (two volumes)",
editor={E.R. Pike and P.C. Sabatier},
year=2001,
pages={37--73},
publisher={Academic Press, London},
note={available at {\tt http://diogenes.iwt.uni-bremen.de/vt/laser/papers/Kress-acustic-scatter-ed-book.ps}}
}

@book{anselone,
author="P. M. Anselone",
title="Collectively compact operator approximation theory",
publisher={Prentice-Hall, Englewood Cliffs, NJ},
year=1971
}

@article{osbornrate,
author="J. Osborn",
title="Spectral Approximation for Compact Operators",
journal="Math. Comput.",
volume=29,
issue={131},
year=1975,
pages={712--725}
}

@article{atkinspec,
author="K. Atkinson",
title="The Numerical Solution of the Eigenvalue Problem for Compact Integral Operators",
journal="Trans. Amer. Math. Soc.",
volume=129,
issue={3},
year=1967,
pages={458--465}
}

@article{atkinrate,
author="K. Atkinson",
title="Convergence rates for approximate eigenvalues of compact integral operators",
journal=sinum,
volume=12,
issue={2},
year=1975,
pages={213--222}
}

@article{tang,
author="Tang, L. and Yoshie, T.",
title="Ultra-high-{Q} three-dimensional photonic crystal nano-resonators",
journal=oe,
year=2007,
pages={17254},
volume=15,
issue=25
}

@article{jolyjing,
author="Joly, P. and Li, J.-R. and Fliss, S.",
title="Exact Boundary Conditions for Periodic Waveguides
Containing a Local Perturbation",
journal="Comm. Comput. Phys.",
year=2006,
volume=1,
issue=6,
pages={945--973}
}

@article{fliss,
author="S. Fliss and Joly, P.",
title="Exact boundary conditions for time-harmonic wave propagation in locally
perturbed periodic media",
journal="Appl. Num. Math.",
year={2008 ({\it in press})}
}

@article{shipman,
author = {Shipman, S. and Venakides, S.},
title="Resonance and Bound States in Photonic Crystal Slabs",
journal="SIAM J. Appl. Math.",
volume=64,
issue=1,
year=2003,
pages={322--342}
}

@article{venakides00,
author={Venakides, S. and Haider, M. A. and Papanicolaou, V.},
journal={SIAM J. Appl. Math.},
year=2000,
title="BOUNDARY INTEGRAL CALCULATIONS OF TWO-DIMENSIONAL
ELECTROMAGNETIC SCATTERING BY PHOTONIC CRYSTAL
{Fabry-Perot} STRUCTURES",
volume=60,
issue=5,
pages={1686--1706}
}

@article{haider02,
title="Boundary-Integral Calculations of Two-Dimensional Electromagnetic Scattering in Infinite Photonic Crystal Slabs: Channel Defects and Resonances",
author="M Haider and S. Shipman and S. Venakides",
journal="SIAM J. Appl. Math.",
volume=62,
year=2002,
number=6,
pages={2129--2148}
}

@article{channeldrop,
author={S. Fan and P. R. Villeneuve and J. D. Joannopoulos and H. A. Haus},
title={Channel drop filters in a photonic crystal},
journal=oe,
volume=3,
pages={4--11},
year=1998
}

@article{metareview,
author={N. M. Litchinitser and V. M. Shalaev},
title={Photonic metamaterials},
journal={Laser Phys. Lett.},
volume=5,
number=6,
pages={411--420},
year=2008
}

@article{PCsolar,
author={P Bermel and C Luo and Lirong Zeng and Lionel C. Kimerling and John D. Joannopoulos},
title={Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals},
journal=oe,
year=2007,
volume=15,
number=25,
pages={16986--17000}
}

@article{yablonovich,
author={E. Yablonovitch},
title={Photonic band-gap structures},
journal={J. Opt. Soc. Am. B},
volume={10},
pages={283--295},
year=1993
}

@article{crutchfield,
author = {W Crutchfield and H Cheng and L Greengard}, 
journal = oe,
title = {Sensitivity analysis of photonic crystal fiber},
pages = {4220--4226},
volume = {12},
year = {2004},
month = {Jan},
}

@article{botten03,
author = {L C Botten and R C McPhedran and N A Nicorovici and A A Asatryan and C M de Sterke and P A Robinson and K Busch and G H Smith and T N Langtry}, 
journal = {Progress in Electromagnetics Research},
title = {Rayleigh Multipole Methods for Photonic Crystal Calculations},
pages = {21--60},
volume = {41},
year = {2003},
month = {Dec},
}

@article{Cheng_pcf04,
author = {H Cheng and W Crutchfield and M Doery and L Greengard}, 
journal = oe,
title = {Fast, accurate integral equation methods for the analysis of photonic crystal fibers I: 
Theory},
pages = {3791--3805},
volume = {12},
year = {2004},
month = {Jan},
}

@Article{Pissoort,
author = {D Pissoort and E Michielssen and F Olyslager and D De Zutter}, 
journal = {Journal of lightwave technology},
title = {Fast analysis of {2D} electromagnetic crystal devices using a periodic Green function approach},
number = {7},
pages = {2294--2308},
volume = {23},
year = {2005},
month = {Jan},
}

@article{Beylkin08,
author = {G Beylkin and C Kurcz and L Monz{\'o}n}, 
journal = {Proc. R. Soc. A},
title = {Fast algorithms for {H}elmholtz {G}reen's functions},
pages = {3301--3326},
volume = {464},
year = {2008},
}

@article{spence,
author={A Spence and C Poulton},
journal=jcp,
title="Photonic band structure calculations using nonlinear
eigenvalue techniques",
year=2005,
volume=204,
pages={65--81}
}

@article{axmann99,
author={W Axmann and P Kuchment},
journal=jcp,
year=1999,
title={An Efficient Finite Element Method for
Computing Spectra of Photonic and
Acoustic Band-Gap Materials},
volume=150,
pages={468--481}
}

@article{dobson99,
author={D C Dobson},
journal=jcp,
year=1999,
title={An Efficient Method for Band Structure Calculations in 2D Photonic Crystals},
volume=149,
pages={363--376}
}

@article{dossou,
author={K Dossou and M Byrne and L C Botten},
journal=jcp,
year=2006,
title={Finite element computation of grating scattering matrices
and application to photonic crystal band calculations},
volume=219,
pages={120--143}
}

@article{johnson01,
author={Steven G. Johnson and J. D. Joannopoulos},
title={Block-iterative frequency-domain methods
for {M}axwell's equations in a planewave basis},
year=2001,
journal=oe,
volume=8,
number=3,
pages={173--190}
}

@book{wilcox,
author={Wilcox, C. H.},
title={Scattering theory for diffraction gratings},
year=1984,
series={Applied Mathematical Sciences, volume 46},
publisher={Springer-Verlag}
}

@article{arens06,
author="T Arens and S N Chandler-Wilde and J A DeSanto",
title="On integral equation and least squares methods for scattering by diffraction gratings",
journal="Commun. Comput. Phys.",
year=2006,
volume=1,
pages={1010--42}
}

@article{zhang03,
author="Bo Zhang and Simon N Chandler-Wilde",
title="Integral equation methods for scattering by infinite rough
surfaces",
journal="Math. Meth. Appl. Sci.",
year=2003,
volume=26,
pages={463--488}
}

@article{CWzhang99,
author="Simon N Chandler-Wilde and Bo Zhang",
title="Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers",
journal="SIAM J. Math. Anal.",
year=1999,
volume=30,
number=3,
pages={559--583}
}

@article{CWnystrom,
title={A {Nystr\"{o}m} method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces},
author={A Meier and T Arens and S N Chandler-Wilde and A Kirsch},
year=2000,
journal={J. Integral Equations Appl.},
volume=12,
pages={281--321}
}

@article{bao95,
title="Finite Element Approximation of Time Harmonic Waves in Periodic Structures",
author={Gang Bao},
journal=sinum,
volume=32,
number=4,
year=1995,
pages={1155--1169}
}

@article{baodobsonrev,
author="Gang Bao and David C. Dobson",
title="Modeling and optimal design of diffractive optical structures",
journal="Surv. Math. Ind.",
volume=8,
year=1998,
pages={37--62}
}

@article{bonnetBDS,
title="Guided Waves by Electromagnetic Gratings and
Non-uniqueness Examples for the Diffraction Problem",
author="{Bonnet-BenDhia, A.-S.} and F Starling",
year=1994,
journal=mmas,
volume=17,
pages={305-338}
}
%author="{Bonnet-BenDhia, A.-S.} and F Starling",
% note the hack to get A.-S. hyphen initials correct in spmpsci bibtex style!
% Initials come before surname in CAREER award references, but other way
% round in BIT Numer Math.

@article{nedelec-starling,
journal={SIAM J. Math. Anal.},
volume=22,
number=6,
pages={1679--1701},
year=1991,
title={Integral equation methods in a quasi-periodic diffraction problem
for the time-harmonic {M}axwell's equations},
author={J. C. {N\'{e}d\'{e}lec} and F. Starling}
}

@inbook{shipmanreview,
title="Resonant scattering by open periodic waveguides",
author="S Shipman",
booktitle="Wave Propagation in Periodic Media: Analysis, Numerical Techniques and Practical Applications",
series="Progress in Computational Physics (PiCP)",
volume=1,
year=2010,
pages={7--50},
publisher={Bentham Science Publishers}
}
%editor="Matthias Ehrhardt",

@book{petit,
editor="R Petit",
title="Electromagnetic Theory of Gratings",
series="Topics in Current Physics",
volume=22,
publisher={Springer-Verlag,Heidelberg},
year=1980
}

@article{horoshenkov,
title={Efficient calculation of two-dimensional periodic and waveguide acoustic {G}reen's functions},
author={K V Horoshenkov and S N Chandler-Wilde},
year=2002,
journal="J. Acoust. Soc. Amer.",
volume=111,
pages={1610--1622}
}

@article{kurkcu,
author={H Kurkcu and F Reitich},
title={Stable and efficient evaluation of periodized {G}reen's functions
for the {H}elmholtz equation at high frequencies},
journal=jcp,
volume=228,
year=2009,
pages={75--95}
}

@article{rayleigh,
author={Lord Rayleigh},
title={On the dynamical theory of gratings},
journal="Proc. R. Soc. Lond. A",
volume=79,
year=1907,
pages={399--416}
}

@article{nicholas,
author="Nicholas, Michael J.",
title="A higher order numerical method for {3-D} doubly periodic
electromagnetic scattering problems",
journal="Commun. Math. Sci.",
volume=6,
year=2008,
number=3,
pages={669--694}
}


@article{elschner,
title={Finite Element Solution of Conical Diffraction Problems},
author={Johannes Elschner and Rainer Hinder and Gunther Schmidt},
journal={Adv. Comput. Math.},
volume=16,
number={2--3},
year=2002,
pages={139--156}
}

@misc{arenshabil,
author={T Arens},
title={Scattering by Biperiodic Layered Media:
   The Integral Equation Approach},
howpublished={Habilitation thesis, Karlsruhe},
year=2010
}

@article{wulu09,
author={Y. Wu and Y. Y. Lu},
title={Analyzing diffraction gratings by a boundary integral equation {N}eumann-to-{D}irichlet map method},
journal={J. Opt. Soc. Am. A},
volume=26,
number=11,
year=2009,
pages={2444--2451}
}


@article{plasmonholes,
author="T.W. Ebbessen and H.J. Lezec and H.F. Ghaemi and T. Thio and P.A. Wolff",
title="Extraordinary optical
   transmission through sub-wavelength hole arrays",
journal="Nature",
volume=391,
year=1998,
pages={667--669}
}

@article{Cmethod,
title={Rigorous and Efficient Grating-Analysis Method Made Easy for Optical Engineers},
journal=ao,
volume=38,
number=2,
pages={304--313},
year=1999,
author={Lifeng Li and Jean Chandezon and G{\'{e}}rard Granet and Jean-Pierre Plumey}
}

@article{qpfdtd,
title={Some Experiences From {FDTD} Analysis of Infinite and Finite Multi-Octave Phased Arrays},
author={Henrik Holter and Hans Steyskal},
journal={IEEE Trans.\ Antennae Prop.},
year=2002,
volume=50,
number=12,
pages={1725--1731}
}

@misc{brunowaves11,
title={Efficient Solution of Acoustic and Electromagnetic Scattering Problems in Three-Dimensional Periodic Media},
author={Oscar P Bruno and Stephen Shipman and Catalin Turc and Stephanos Venakides},
year=2011,
journal={Proceedings of WAVES2011: the 10th international conference
on the mathematical and numerical aspects of waves.}
}

@article{brunohaslam09,
title={  Efficient high-order evaluation of scattering by periodic surfaces: deep gratings, high frequencies,              and glancing incidences},
author={Oscar P Bruno and Michael C Haslam},
year=2009,
journal={J. Opt. Soc. Am. A},
volume=26,
number=3,
pages={658--668}
}



% ====================== Diffraction and photonics applications ============ 

@book{planarlightwave,
title={Frontiers in Planar Lightwave Circuit Technology
Design, Simulation, and Fabrication},
author={Siegfried Janz and Jiri Ctyroky and Stoyan Tanev},
series={NATO Science Series II: Mathematics, Physics and Chemistry,
volume 216},
publisher={Springer Netherlands},
year=2006
}

@article{acoustmeta,
author={Shu Zhang and Yin, Leilei and Fang, Nicholas},
title={Focusing Ultrasound with an Acoustic Metamaterial Network},
journal=prl,
year=2009,
volume=102,
pages=194301
}

@article{vlasov,
title={Active control of slow light on a chip with photonic crystal waveguides},
author={Yurii A. Vlasov and Martin O'Boyle and  Hendrik F. Hamann and Sharee J. McNab},
journal={Nature},
volume=438,
pages={65--69},
year=2005
}

%other authors: M. Key , J. Britten , R. Beach , G. Beer , C. Brown , S. Bryan , J. Caird , T. Carlson , J. Crane , J. Dawson , A.C. Erlandson , D. Fittinghoff , M. Hermann , C. Hoaglan , A. Iyer , L. Jones II , I. Jovanovic , A. Komashko , O. Landen , Z. Liao , W. Molander , S. Mitchell , E. Moses , N. Nielsen , H-H. Nguyen , J. Nissen , S. Payne , D. Pennington , L. Risinger , M. Rushford , K. Skulina , M. Spaeth , B. Stuart , G. Tietbohl and B. Wattellier
@article{NIF,
title={An overview of {LLNL} high-energy short-pulse technology for advanced radiography of laser fusion experiments},
author={C. P. J. {Barty, et al.}},
journal={Nuclear Fusion},
volume=44,
number=12,
pages={S266},
year=2004
}

@article{interconnects,
author={A. Shacham and K. Bergman and L. P. Carloni},
title={Photonic Networks-on-Chip for Future Generations of Chip Multi-Processors},
journal={IEEE Trans. Computers},
volume=57,
number=9,
year=2008,
pages={1246--1260}
}

% This is for lower-power-consumption of optical interconnects....
@misc{consumption,
title="Smart 2020: enabling the low carbon economy in the information age",
author="{The Climate Group for the Global e-Sustainability Initiative}",
note={\verb+http://www.smart2020.org/_assets/files/03_Smart2020Report_lo_res.pdf+},
year=2008
} 

@article{pendry,
year=2006,
volume=312,
number=5781,
pages={1780--1782},
journal={Science},
title={Controlling Electromagnetic Fields},
author={J. B. Pendry and D. Schurig and D. R. Smith}
}

@article{kohncloak,
author={R. V. Kohn and D. Onofrei and M. S. Vogelius and M. I. Weinstein},
title={Cloaking via change of variables for the {H}elmholtz equation},
journal=cpam,
volume=63,
year=2010,
pages={973--1016}
}

@article{scatterometry,
author={R Model and A Rathsfeld and H Gross and M Wurm and B Bodermann},
title={A scatterometry inverse problem in optical mask metrology},
year=2008,
journal={J. Phys.: Conf. Ser.},
volume=135,
pages=012071
}

@inproceedings{refmodels,
author={Gregory L. Wojcik and John Mould Jr. and Egon Marx† and Mark P. Davidson},
title={Numerical Reference Models for Optical Metrology Simulation},
booktitle={SPIE Microlithography ‘92: IC Metrology, Inspection, and Process Control VI, \#1673-06},
year=1992
}

@article{waterwave,
journal={J. Fluid Mech.},
year=2006,
volume=548,
pages={237--256},
title={Water-wave scattering by a periodic array of arbitrary bodies},
author={M. A. Peter and M. H. Meylan and C. M. Linton}
}

@misc{CWnote,
author={S. Chandler-Wilde},
year=2010,
note={personal communication}
}

% ------------------------------------- analysis of PDEs in complex plane, Vekua

@article {Ga53,
    AUTHOR = {Garabedian, P. R.},
     TITLE = {Applications of analytic continuation to the solution of
              boundary value problems},
   JOURNAL = {J. Rational Mech. Anal.},
    VOLUME = {3},
      YEAR = {1954},
     PAGES = {383--393},
   MRCLASS = {31.0X},
  MRNUMBER = {MR0061222 (15,792d)},
MRREVIEWER = {H. G. Garnir},
}

@article {Le59,
    AUTHOR = {Lewy, Hans},
     TITLE = {On the reflection laws of second order differential equations
              in two independent variables},
   JOURNAL = {Bull. Amer. Math. Soc.},
    VOLUME = {65},
      YEAR = {1959},
     PAGES = {37--58},
   MRCLASS = {35.00},
  MRNUMBER = {MR0104048 (21 \#2810)},
MRREVIEWER = {M. Schiffer},
}

@article {Mi80,
    AUTHOR = {Millar, Robert F.},
     TITLE = {The analytic continuation of solutions to elliptic boundary
              value problems in two independent variables},
   JOURNAL = {J. Math. Anal. Appl.},
  FJOURNAL = {Journal of Mathematical Analysis and Applications},
    VOLUME = {76},
      YEAR = {1980},
    NUMBER = {2},
     PAGES = {498--515},
      ISSN = {0022-247X},
     CODEN = {JMANAK},
   MRCLASS = {35C15 (35A20 35B60 35J25)},
  MRNUMBER = {MR587358 (81j:35025)},
MRREVIEWER = {Manfred W. Kracht},
}

@article {Mi86,
    AUTHOR = {Millar, Robert F.},
     TITLE = {Singularities and the {R}ayleigh hypothesis for solutions to
              the {H}elmholtz equation},
   JOURNAL = {IMA J. Appl. Math.},
  FJOURNAL = {IMA Journal of Applied Mathematics},
    VOLUME = {37},
      YEAR = {1986},
    NUMBER = {2},
     PAGES = {155--171},
      ISSN = {0272-4960},
     CODEN = {IJAMDM},
   MRCLASS = {35P25 (35J05 76Q05 78A25)},
  MRNUMBER = {MR983524 (90b:35187)},
MRREVIEWER = {A. Elcrat},
}

@article {He57,
    AUTHOR = {Henrici, Peter},
     TITLE = {A survey of {I}. {N}. {V}ekua's theory of elliptic partial
              differential equations with analytic coefficients},
   JOURNAL = {Z. Angew. Math. Phys.},
  FJOURNAL = {Zeitschrift f\"ur Angewandte Mathematik und Physik. ZAMP.
              Journal of Applied Mathematics and Physics. Journal de
              Math\'ematiques et de Physique Appliqu\'ees},
    VOLUME = {8},
      YEAR = {1957},
     PAGES = {169--203},
      ISSN = {0044-2275},
   MRCLASS = {35.0X},
  MRNUMBER = {MR0085427 (19,38a)},
MRREVIEWER = {E. T. Copson},
}

@article{schryer,
   AUTHOR = {Schryer, N. L.},
     TITLE = {Constructive approximation of solutions to linear elliptic
              boundary value problems},
   JOURNAL = {SIAM J. Numer. Anal.},
  FJOURNAL = {SIAM Journal on Numerical Analysis},
    VOLUME = {9},
      YEAR = {1972},
     PAGES = {546--572}
}



@article {Ei74,
    AUTHOR = {Eisenstat, S. C.},
     TITLE = {On the rate of convergence of the {B}ergman-{V}ekua method for
              the numerical solution of elliptic boundary value problems},
   JOURNAL = {SIAM J. Numer. Anal.},
  FJOURNAL = {SIAM Journal on Numerical Analysis},
    VOLUME = {11},
      YEAR = {1974},
     PAGES = {654--680},
      ISSN = {1095-7170},
   MRCLASS = {65N25 (35C15)},
  MRNUMBER = {MR0375805 (51 \#11995)},
MRREVIEWER = {I. Aganovic},
}

@book {Da74,
    AUTHOR = {Davis, Philip J.},
     TITLE = {The {S}chwarz function and its applications},
      NOTE = {The Carus Mathematical Monographs, No. 17},
 PUBLISHER = {The Mathematical Association of America, Buffalo, N. Y.},
      YEAR = {1974},
     PAGES = {xi+228},
   MRCLASS = {30A30},
  MRNUMBER = {MR0407252 (53 \#11031)},
MRREVIEWER = {I. N. Baker},
}

@article{bookrevshapiro,
author="Korevaar, J.",
title={Book review of {\em The {S}chwarz function and its generalization to higher dimensions} by {H.} {S.} {S}hapiro},
journal="Bull. Amer. Math. Soc.",
volume=31,
year=1994,
pages={112--116}
} 


@article{melenkPUM,
author="Melenk, J. M. and Babuska, I.",
title="Approximation with harmonic and generalized harmonic polynomials in the partition of unity method",
journal="Comput. Assist. Mech. Eng. Sci.",
volume=4,
year=1997,
pages={607--632}
}

@book{vekua,
author="Vekua, I. N.",
title="Novye metody rezhenija elliptickikh uravnenij, (OGIZ,
Moscow and Leningrad, 1948); English
translation: New methods for solving elliptic equations",
publisher="North-Holland",
year=1967
}

@article{millaraxi,
author="Millar, R. F.",
title="Singularities of Solutions to Exterior Analytic Boundary Value Problems for the Helmholtz Equation in Three Independent Variables. {II}: {T}he Axisymmetric Boundary",
year=1979,
journal="SIAM J. Math. Anal.",
volume=10,
issue=4,
pages={682--694}
}


% -------------------------------------------------------- general numerical

@Book{LAPACK,
	Address = "Philadelphia, PA, USA",
	Isbn = "0-89871-447-8",
	Publisher = "Society for Industrial and Applied Mathematics",
	author = "E. Anderson and Z. Bai and C. Bischof and L. S. Blackford and J. Demmel and Jack J. Dongarra and J. Du Croz and A. Greenbaum and S. Hammarling and A. McKenney and D. Sorensen",
	title = "LAPACK Users{'} guide (third ed.)",
	year = 1999
}

@book{na,
author="Kress, R.",
title="Numerical Analysis",
series="Graduate Texts in Mathematics \#181",
year=1998,
publisher="Springer-Verlag"
}

@article{lnt92,
author="L.N. Trefethen",
title="The definition of numerical Analysis",
journal="SIAM News",
month="November",
year=1992,
note="{\tt http://people.maths.ox.ac.uk/trefethen/essays.html}"
}

@article{hale,
title="Computing {$A^\alpha$}, {$\log(A)$}, and related MATRIX FUNCTIONS
                 BY CONTOUR INTEGRALS",
author="N Hale and N J Higham and L N Trefethen",
journal=sinum,
year=2008,
volume=46,
number=5,
pages={2505­-2523}
}

@article{bromwich,
journal="Math. Comput.",
volume=76,
number=259,
year=2007,
pages={1341­-1356},
title="                 PARABOLIC AND HYPERBOLIC CONTOURS
              FOR COMPUTING THE BROMWICH INTEGRAL",
author="J. A. C. Weideman and L. N. Trefethen"
}


@article{weidemanrev,
title="Numerical Integration of Periodic Functions: A Few Examples",
author="J. A. C. Weideman",
journal="Amer. Math. Monthly",
volume=109,
number=1,
year=2002,
pages={21--36}
}



@book {numrec,
    AUTHOR = {Press, William H. and Teukolsky, Saul A. and Vetterling,
              William T. and Flannery, Brian P.},
     TITLE = {Numerical recipes in {C}},
edition = {2nd},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {2002},
}

@article{ross,
author={Barnett, A. R. and Feng, D. H. and Steed, J. W. and Goldfarb, L. J. B.},
year=1974,
journal=cpc,
volume=8,
pages={377--395},
title={Coulomb wave functions for all real $\eta$ and $\rho$}
}


% here: no other names listed:
@misc{GSL,
author={{M. Galassi {\it et al.}}},
title={{GNU} {S}cientific {L}ibrary {R}eference {M}anual},
edition={2nd},
note={{\tt http://www.gnu.org/software/gsl}}
}

@article{fix,
author="Fix, G. and Heiberger, R.",
title="An algorithm for the ill-conditioned
generalized eigenvalue problem",
journal="SIAM J. Num. Anal.",
year=1972,
volume=9,
pages={78--88}
}

@book{parlett,
author="Parlett, B. N.",
title="The Symmetric Eigenvalue Problem",
year=1980,
publisher="Prentice-Hall",
address="Englewood Cliffs, NJ"
}

@book {golubvanloan,
    AUTHOR = {Golub, Gene H. and Van Loan, Charles F.},
     TITLE = {Matrix computations},
    SERIES = {Johns Hopkins Studies in the Mathematical Sciences},
   EDITION = {Third},
 PUBLISHER = {Johns Hopkins University Press},
   ADDRESS = {Baltimore, MD},
      YEAR = {1996},
     PAGES = {xxx+698},
      ISBN = {0-8018-5413-X; 0-8018-5414-8},
   MRCLASS = {65-02 (65Fxx)},
  MRNUMBER = {MR1417720 (97g:65006)},
}


@article{rbf,
author="Driscoll, T. A. and Fornberg, B.",
title="Interpolation in the limit of increasingly flat radial basis functions",
journal="Computers Mathematics Appl.",
volume=43,
issue={3--5},
year=2002,
pages={413--422}
}

@book {tref,
    AUTHOR = {Trefethen, Lloyd N.},
     TITLE = {Spectral methods in {MATLAB}},
    SERIES = {Software, Environments, and Tools},
    VOLUME = {10},
 PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)},
   ADDRESS = {Philadelphia, PA},
      YEAR = {2000},
     PAGES = {xviii+165}
}

@book{nla,
author="Trefethen, L. N. and Bau III, D.",
title="Numerical Linear Algebra",
year=1997,
publisher="SIAM"
}

@misc{matlab,
AUTHOR={{The MathWorks, Inc.}},
title={{MATLAB} software},
note={{\tt http://www.mathworks.com/matlab}},
year={Copyright (c) 1984--2011},
}

@article{helsing_corner,
author="Helsing, J and Ojala, R.",
year=2008,
journal="J. Comput. Phys.",
title="Corner singularities for elliptic problems: Integral equations, graded 
meshes, quadrature, and compressed inverse preconditioning",
volume=227,
pages={8820--8840}
}

@article{bremer10,
title={Efficient discretization of {L}aplace boundary integral equations on polygonal domains},
author={J. Bremer and V. Rokhlin},
journal=jcp,
year=2010,
volume=229,
pages={2507--2525}
}

@article{beale,
author="Beale, J and Lai, M.-C.",
year=2001,
journal="SIAM J. Numer. Anal.",
title="A method for computing nearly singular integrals",
volume=38,
pages={1902--1925}
}

@article{kapur,
author="Kapur, S. and Rokhlin, V.",
year=1997,
journal="SIAM J. Numer. Anal.",
title="High-order corrected trapezoidal quadrature rules for singular functions",
volume=34,
pages={1331--1356}
}

@article{alpert,
author="Alpert, B. K.",
year=1999,
journal="SIAM J. Sci. Comput.",
title="Hybrid {G}auss-trapezoidal quadrature rules",
volume=20,
pages={1551--1584}
}

@article{mayo,
author="Mayo, A.",
year=1985,
journal="SIAM J. Sci. Stat. Comput.",
title="Fast high order accurate solution of {L}aplace's equation on irregular regions ",
volume=6,
pages={144--157}
}

@article{bremer,
author="Bremer, J and Rokhlin, V. and Sammis, I.",
year=2009,
journal="Yale University Department of Computer Science Technical Report 1420",
title="Universal quadratures for boundary integral equations on two-dimensional 
domains with corners"
}


@article{helsing,
author="Helsing, J",
year=2009,
journal="J. Comput. Phys.",
title="Integral equation methods for elliptic problems with boundary conditions of mixed type",
volume=228,
pages={8892--8907}
}

@misc{helsingtut,
author="Helsing, J",
year=2012,
title="Solving integral equations on piecewise smooth boundaries using the {RCIP} method: a tutorial",
note="preprint, 34 pages, {\tt arXiv:1207.6737v3}"
}

@article{helsing_close,
author="Helsing, J and Ojala, R.",
year=2008,
journal="J. Comput. Phys.",
title="On the evaluation of layer potentials close to their sources",
volume=227,
pages={2899--2921}
}

@inproceedings{davis59,
year=1959,
author={P. J. Davis},
title="On the numerical integration of periodic analytic functions",
booktitle={Proceedings of a Symposium on Numerical Approximations},
editor={R. E. Langer},
publisher={University of Wisconsin Press}
}

@article{hunter71,
year=1971,
author={D. B. Hunter},
title={The evaluation of integrals of periodic analytic functions},
journal=bit,
volume=11,
pages={175--180}
}

% ------------------ Fast Direct Solvers -----------------------------------

@misc{gillman,
year=2011,
author={A. Gillman and P. Young and P. G. Martinsson},
title="A direct solver with {$O(N)$} complexity for integral equations on one-dimensional domains",
notes={{\em in review}}
} 

%%%  Adrianna's references
@article{m2011_1D_survey,
    AUTHOR = {Gillman, A. and Young, P. and Martinsson, P.G.},
     TITLE = {A direct solver with {$O(N)$} complexity for integral equations on one-dimensional domains},
     JOURNAL= {Frontiers of Mathematics in China},
    VOLUME = {7},
    NUMBER = {2},
     PAGES = {217-247},
     YEAR = {2012},
}

@article{hackbusch,
  author = {W. Hackbusch},
  title = {A Sparse Matrix Arithmetic Based on {H}-Matrices;
           {P}art {I}: {I}ntroduction to {H}-Matrices},
  journal = {Computing},
  volume = {62},
  pages = {89--108},
  year = {1999}
}

@book{2010_borm,
AUTHOR = {B\"orm, S.},
TITLE = {Efficient Numerical Methods for Non-local Operators: $\mathcal{H}^2$-Matrix Compression,
         Algorithms and Analysis},
YEAR = {2010},
PUBLISHER = {European Mathematics Society}
}

@article {mdirect,
    AUTHOR = {Martinsson, P.G. and Rokhlin, V.},
     TITLE = {A fast direct solver for boundary integral equations in two dimensions},
   JOURNAL = {J. Comp. Phys.},
    VOLUME = {205},
    NUMBER = {1},
      YEAR = {2005},
     PAGES = {1--23},
}
@incollection {BCR,
    AUTHOR = {Beylkin, G. and Coifman, R. and Rokhlin, V.},
     TITLE = {Wavelets in numerical analysis},
 BOOKTITLE = {Wavelets and their applications},
     PAGES = {181--210},
 PUBLISHER = {Jones and Bartlett},
   ADDRESS = {Boston, MA},
      YEAR = {1992},
}

@article {1996_mich_elongated,
    AUTHOR = {Michielssen, E. and Boag, A. and Chew, W. C.},
     TITLE = {Scattering from elongated objects: direct solution in ${O}({N}\log^{2}{N})$ operations},
   JOURNAL = {IEE Proc. Microw. Antennas Propag.},
    VOLUME = {143},
      YEAR = {1996},
    NUMBER = {4},
     PAGES = {277 -- 283},
}

@article {1994_starr_rokhlin,
    AUTHOR = {P. Starr and V. Rokhlin},
     TITLE = {On the numerical solution of two-point boundary value
              problems. {II}},
   JOURNAL = {Comm. Pure Appl. Math.},
  FJOURNAL = {Communications on Pure and Applied Mathematics},
    VOLUME = {47},
      YEAR = {1994},
    NUMBER = {8},
     PAGES = {1117--1159},
}

@misc{2011_hao_nystrom,
AUTHOR = {Hao, S. and Martinsson, P.G. and Young, P.},
TITLE = {High-order accurate {N}ystr\"om discretization of integral equations with weakly singular kernels on smooth curves in the plane},
NOTE = {ar{X}iv.org report \#1112.6262},
YEAR = {2011}
}

@misc{ho,
AUTHOR = {Ho, K. L. and Greengard, L. },
TITLE = {A fast direct solver for structured linear systems by recursive skeletonization},
NOTE = {To appear in SIAM J. on Scientific Computing},
YEAR = {2012}
}
@book {golub,
    AUTHOR = {G. Golub and C. Van Loan},
     TITLE = {Matrix computations},
    SERIES = {Johns Hopkins Studies in the Mathematical Sciences},
   EDITION = {Third},
 PUBLISHER = {Johns Hopkins University Press},
   ADDRESS = {Baltimore, MD},
      YEAR = {1996},
     PAGES = {xxx+698},
      ISBN = {0-8018-5413-X; 0-8018-5414-8},
}
@incollection {2007_shiv_sheng,
    AUTHOR = {Sheng, Z. and Dewilde, P. and Chandrasekaran, S.},
     TITLE = {Algorithms to solve hierarchically semi-separable systems},
 BOOKTITLE = {System theory, the Schur algorithm and multidimensional
              analysis},
    SERIES = {Oper. Theory Adv. Appl.},
    VOLUME = {176},
     PAGES = {255--294},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2007},
}

@article {gu_divide,
    AUTHOR = {Chandrasekaran, S. and Gu, M.},
     TITLE = {A divide-and-conquer algorithm for the eigendecomposition of
              symmetric block-diagonal plus semiseparable matrices},
   JOURNAL = {Numer. Math.},
  FJOURNAL = {Numerische Mathematik},
    VOLUME = {96},
      YEAR = {2004},
    NUMBER = {4},
     PAGES = {723--731},
      ISSN = {0029-599X},
     CODEN = {NUMMA7},
}

% -------------------------------------------------- PDEs (non-numerical)

@article {rellich,
    AUTHOR = {Rellich, Franz},
     TITLE = {Darstellung der {E}igenwerte von {$\Delta u+\lambda u=0$}
              durch ein {R}andintegral},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {46},
      YEAR = {1940},
     PAGES = {635--636}
}
%   MRCLASS = {36.0X},
%  MRNUMBER = {MR0002456 (2,56d)},
%MRREVIEWER = {K. Friedrichs},

@book {garab,
    AUTHOR = {Garabedian, P. R.},
     TITLE = {Partial differential equations},
 PUBLISHER = {John Wiley \& Sons Inc.},
   ADDRESS = {New York},
      YEAR = {1964},
     PAGES = {xii+672},
   MRCLASS = {35.00},
  MRNUMBER = {MR0162045 (28 \#5247)},
MRREVIEWER = {L. E. Payne},
}

@book{folland,
author="Folland, G. B.",
title="Introduction to Partial Differential Equations",
edition="2nd",
year=1995,
publisher="Princeton University Press"
}

@book{coltonpde,
author="Colton, David",
title="Partial Differential Equations. An Introduction",
year=1988,
publisher="Dover"
}

@book{stakgold,
author="Stakgold, I.",
title="Boundary Value problems of mathematics physics. Volumes I \& II",
year=1967,
publisher={SIAM Classics in Applied Math \#29},
} 

@book{logan,
author="Logan, D.",
title="Applied Mathematics",
edition="4th",
year=2006,
publisher="Wiley"
}

@book {CK83,
    AUTHOR = {Colton, David and Kress, Rainer},
     TITLE = {Integral equation methods in scattering theory},
 PUBLISHER = {Wiley},
      YEAR = {1983}
}

@book {coltonkress,
    AUTHOR = {Colton, David and Kress, Rainer},
     TITLE = {Inverse acoustic and electromagnetic scattering theory},
    SERIES = {Applied Mathematical Sciences},
    VOLUME = {93},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1998}
}

@book{LIE,
author={Kress, Rainer},
title={Linear Integral Equations},
    SERIES = {Applied Mathematical Sciences},
    VOLUME = {82},
edition={Second},
publisher={Springer},
year=1999
}

@book {lions+magenes,
    AUTHOR = {Lions, J.-L. and Magenes, E.},
     TITLE = {Probl\`emes aux limites non homog\`enes et applications.
              {V}ol. 3},
      NOTE = {Travaux et Recherches Math\'ematiques, No. 20},
 PUBLISHER = {Dunod},
   ADDRESS = {Paris},
      YEAR = {1970},
     PAGES = {xvii+328},
   MRCLASS = {47F05 (35R99)},
  MRNUMBER = {MR0291887 (45 \#975)},
MRREVIEWER = {R. S. Freeman},
}

@book{mclean,
author="Mc{L}ean, W. C. H.",
title="Strongly elliptic systems and boundary integral equations",
year=2000,
publisher="Cambridge University Press"
}

@book{evanspde,
author="Evans, L. C.",
title="Partial Differential Equations",
   SERIES = {Graduate Studies in Mathematics},
    VOLUME = {19},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {1998},
     PAGES = {xviii+662}
}

@article{mitrea,
author="Mitrea, M",
year=1996,
journal="J. Math. Anal. Appl.",
title="Boundary Value Problems and {H}ardy Spaces
Associated to the {H}elmholtz Equation in {L}ipschitz Domains",
volume=202,
pages={819--842}
}

@book {guentherlee,
    AUTHOR = {Guenther, Ronald B. and Lee, John W.},
     TITLE = {Partial differential equations of mathematical physics
              and integral equations},
 PUBLISHER = {Prentice Hall},
   ADDRESS = {Englewood Cliffs, New Jersey},
      YEAR = {1988},
     PAGES = {},
      ISBN = {},
   MRCLASS = {},
  MRNUMBER = {},
MRREVIEWER = {}
}

@book{bdip,
author={W. E. Boyce and R. C. DiPrima},
title={Elementary Differential Equations and Boundary Value Problems},
edition={8th Ed.},
year=2004,
publisher={Wiley}
}


@article{JK, 
author= "D. Jerison, C. Kenig",
title="The inhomogeneous {D}irichlet problem in {L}ipschitz domains",
journal="J. Funct. Anal.",
volume=130,
year=1995,
pages={161--219}
}

@book{PolyaSzego,
author="G. P\'olya and G. Szego", 
title="Isoperimetric inequalities in mathematical physics",
year=1951,
publisher="Princeton university press",
address="Princeton, NJ",
series="Annals of Mathematics Studies, no. 27"
}

@article{Ancona, 
author= "A. Ancona",
title="A note on the {R}ellich formula in {L}ipschitz domains",
journal="Pub. Mathem\`atiques",
volume=42,
year=1998,
pages={223--237}
}

@book{mikhlinbook,
author="S G Mikhlin",
title="Integral equations",
edition="2nd",
publisher="MacMillan, New York",
year=1964
}

@book{taodisp,
author="T Tao",
title="Nonlinear dispersive equations: local and global analysis",
publisher="AMS",
bookseries="CBMS regional conference series in mathematics",
year=2006
}

@book{TaylorI,
author="Taylor, M. E.",
title="Partial Differential Equations: Basic Theory",
year=1996,
address="Berlin",
publisher="Springer"
}



% ------------------------------------------------------------ stats

@book {bayes,
    AUTHOR = {Sivia, D. S.},
     TITLE = {Data analysis},
    SERIES = {Oxford Science Publications},
 PUBLISHER = {The Clarendon Press Oxford University Press},
   ADDRESS = {New York},
      YEAR = {1996},
     PAGES = {xii+189},
   MRCLASS = {62-01 (62-07)},
  MRNUMBER = {MR1420864 (97k:62003)},
}

@book{jaynes,
author="Jaynes, E.T.",
title="Probability theory: the logic of science",
publisher="Cambridge University Press",
editor="Bretthorst, G. Larry",
year=2003
}

@book{complexsys,
author={G. Leibon and S. Pauls and D. N. Rockmore and R. Savell AND M. Herron},
title="Statisical Learning for Complex Systems: an Example-driven Introduction",
year=2010
}

@book{larsen,
author="Larsen, R. J. and Marx, M. L.",
title="An Introduction to Mathematical Statistics and its Applications",
edition="4th",
publisher="Prentice-Hall",
year=2002
}

% ---------------------------------------------------------- math bio / ecology

@book{mhra,
author="Moorcroft, P. R. and Lewis, M. A.",
title="Mechanistic home range analysis",
series="Monographs in population biology",
publisher="Princeton University Press",
year={2006},
address="Princeton, NJ"
}

@phdthesis{moorcroftthesis,
author="Moorcroft, P. R.",
title="Territoriality and carnivore home ranges",
school="Dept.\ of Ecology and Evolutionary Biology, Princeton University",
year=1997
}

@article{moorcroftroy,
author="Moorcroft, P. R. and Lewis, M. A. and Crabtree, R. L.",
year="2006",
title="Mechanistic home range
models predict spatial patterns and dynamics of coyote territories in
Yellowstone",
journal="Proc. Royal Soc. Ser. B",
volume="273",
pages="1651--1659"
}

% paul refs...
@article{turchin,
author="Turchin, P.",
title="Translating foraging movements in heterogeneous environments into
the spatial distribution of foragers",
journal="Ecology",
volume="72",
pages="1253--1266",
year="1991"
}

@article{kareiva,
author="Kareiva, P.",
title="Experimental and Mathematical Analyses of Herbivore Movement: Quantifying the Influence of Plant Spacing and Quality on Foraging Discrimination",
journal="Ecological Monographs",
volume=52,
issue=3,
year=1982,
pages="261--282"
}

@article{patlak,
author="Patlak, C.",
year=1953,
title="Random walk with persistence and external bias",
journal="Bull. Math. Biophys.",
volume="15",
pages="311--338"
}

% the original RSA paper according to Lewis-Moorcroft.
@article{johnsonrsa,
author="Johnson, D. H.",
title="The comparison of usage and availability measurementts for evaluating resource preference",
journal="Ecology",
volume=61,
issue=1,
pages="65--71",
year=1980
}

@book{manly,
author="Manly, B. F. J. and McDonald, L. L. and Thomas, D. L. and McDonald T. L. and Erickson, W. P.",
title="Resouce selection by animals: statistical design and analysis
for field studies",
edition="2nd",
publisher="Kluwer",
address="Dordrecht, The Netherlands",
year={2002}
}


@book{okubo,
author="Okubo, A.",
title="Diffusion and ecological problems",
publisher="Springer-Verlag",
year={1980}
}

@article{othmer,
author="Othmer, H. and Dunbar, S. R. and Alt, W.",
title="Models of dispersion in biological systems",
journal="J. Math. Biol.",
volume=26,
pages="263--298",
year=1988
}

@article{boycerev,
author="Boyce, M. S. and McDonald, L. L.",
journal="Trends in Ecology and Evolution",
title="Relating populations to habitats using resource selection functions",
volume=14,
pages="268--272",
year=1999
}
 
 
@article{thermal,
author="Giuggioli, L. and Abramson, G. and Kenkre, V. M. and
Parmenter, R. R. and Yates, T. L.",
title="Theory of home range estimation from displacement measurements
of animal populations",
journal="J. Theor. Biol.",
volume="240",
pages="126--135",
year={2006}
}

@article{white,
author="White, K. A. J. and Lewis, M. A. and Murray, J. D.",
title="A model for wolf-pack territory formation and maintenance",
journal="J. Theor. Biol.",
volume="178",
pages="26--43",
year=1996
}

@article{lewis,
author="Lewis, M. A. and White, K. A. J. and Murray, J. D.",
title="Analysis of a model for wolf territories",
journal="J. Math. Biol.",
volume=35,
pages="749--774",
year=1997
}


@book {stoc,
    AUTHOR = {Gardiner, Crispin W.},
     TITLE = {Handbook of stochastic methods for physics,
chemistry, and the natural sciences, 3rd ed.},
    SERIES = {Springer Series in Synergetics},
    VOLUME = {13},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2004},
   MRCLASS = {00A69 (60-01 81C20 82A31)},
}

@book {meyntweedie,
AUTHOR={Meyn, S. P. and Tweedie, R. L.},
title = "Markov Chains and Stochastic Stability",
publisher = {Springer-Verlag},
year = {1993},
ADDRESS = {London}
}

@article{arthur,
author="Arthur, S. M. and Manly, B. F. J. and McDonald, L. .L. and
Garner, G. W.",
title="Assessing habitat selection when availability changes",
journal="Ecology",
year=1996,
volume=77,
issue=1,
pages={215--227}
}

@article{compton,
author="Compton, B. W. and Rhymer, J. M. and McCollough, M.",
title="Habitat selection by wood turtles ({\em clemmys insculpta}):
and application of paired logistic regression",
journal="Ecology",
year=2002,
volume=83,
issue=3,
pages={833--843}
}

@article{boyce,
author="Boyce, M. S. and Mao, J. S. and Merrill, E. M. and Fortin, D.",
title="Scale and heterogeneity in habitat selection by elk in {Yellowstone
National Park}",
journal="{\'{E}coscience}",
year=2002,
volume=10,
issue=4,
pages={421--431}
}

@article{fortin,
author="Fortin, D. and Beyer, H. L. and Boyce, M. S. and Smith, D. W.
and Duchesne, T. and Mao, J.",
title="Wolves influence elk movements: behavior shapes a trophic cascade in {Yellowstone National Park}",
journal="Ecology",
year=2005,
volume=86,
issue=5,
pages={1320--1330}
}

@article{forester,
author="Forester, J. D. and Ives, A. R. and Turner, M. G. and Anderson, D. P. and Fortin, D. and Beyer, H. L. and Smith, D. W. and Boyce, M. S.",
title="State-space models link elk movement patterns to landscape characteristics in {Yellowstone National Park}",
journal="Ecological Monographs",
year=2007,
volume=77,
issue=2,
pages={285--299}
}

@article{johnson,
author="Johnson, C. J. and Parker, K. L. and Heard, D. C. and Gillingham, M. P.",
title="A multiscale behavioral approach to understanding the movements of woodland caribou",
journal="Ecological Applications",
year=2002,
volume=12,
issue=6,
pages={1840--1860}
}


% ---------------------------------------------- image tracking / Gladfelter

@article{sbal,
author="Sbalzarini, I. F. and Koumoutsakos, P.",
title="Feature point tracking and trajectory analysis
for video imaging in cell biology",
journal="J. Struct. Biol.",
year=2005,
volume=151,
pages={182--195}
}

@article{chentrack,
author="Chen, X. and Zhou, W. and Wong, S. T. C.",
title="Automated Segmentation, Classification, and Tracking of
Cancer Cell Nuclei in Time-Lapse Microscopy",
journal="IEEE Trans. Biomed. Eng.",
year=2006,
volume=53,
issue=4,
pages={762--766}
}

@article{olsen,
author="Olsen, M. and Bourdon, C. J.",
title="Out-of-Plane Motion Effects in
Microscopic Particle Image
Velocimetry",
journal="J. Fluids Eng.",
year=2003,
volume=125,
pages={895--901}
}

@article{mitotic,
author="Harder, N. and Mora-Berm\'{u}dez, F. and Godinez, W. J. and Ellenberg, J. and  Eils, R. and Rohr, K.",
title="DETERMINATION OF MITOTIC DELAYS IN {3D} FLUORESCENCE MICROSCOPY IMAges
   OF HUMAN CELLS USING AN ERROR-CORRECTING FINITE STATE MACHINE",
journal="Proc. IEEE Internat. Symp. Biomed. Imaging",
year=2007,
pages={1044--47}
}

@article{gladfelterrev,
author="Gladfelter, A. S.",
title="Nuclear anarchy: asynchronous mitosis in multinucleated
fungal hyphae",
journal="Curr. Opin. Microbiol.",
year=2006,
volume=9,
issue=6,
pages={547--552}
}


@article{gladfelter,
author="Gladfelter, A. S. and Hungerbuehler, A. K. and Philippsen, P.",
title="Asynchronous mitoses in multinucleated cells",
journal="J. Cell Biol.",
year=2006,
volume=172,
issue=3,
pages={347--362}
}



% ------------------------------------------------ DOT biomedical optics
@article{arrrev,
author={Arridge, S. R.},
title ={Optical tomography in medical imaging},
year=1999,
journal="Inverse problems",
volume=15,
pages="R41--R93"
}

% overview
@article{boasrev,
author={Boas, D. A. and Brooks, D. H. and Miller, E. L. and DiMarzio, C. A. and Kilmer, M. and Gaudette, R. J. and Zhang, Q.},
title="Imaging the body with diffuse optical tomography",
journal="IEEE Signal Processing Magazine",
year=2001,
volume=18,
issue=6,
pages={57--75}
}

% review all brain imaging optical methods
@article{hillmanrev,
author="Hillman, E. M. C.",
title="Optical Brain Imaging In-vivo: Techniques and Applications from Animal to Man",
journal={J. Biomed. Opt.},
volume=12,
issue=5,
pages=051402,
year=2007
}


% ============================================= NUMERICAL ANALYSIS

@article{boyd,
journal=sinum,
year=2002,
author={J. P. Boyd},
title={Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding},
volume=40,
number=5,
pages={1665--1682}
}

% -------------------------------------------------- general math

@book{a+s,
  author =       "Milton Abramowitz and Irene A. Stegun",
  title =        "Handbook of Mathematical Functions with
                  Formulas, Graphs, and Mathematical Tables",
  publisher =    "Dover",
  year =         1964,
  address =      "New York",
  edition =      "10th"
}

@book {CoHi53,
    AUTHOR = {Courant, R. and Hilbert, D.},
     TITLE = {Methods of mathematical physics. {V}ol. {I}},
 PUBLISHER = {Interscience Publishers, Inc., New York, N.Y.},
      YEAR = {1953},
     PAGES = {xv+561},
   MRCLASS = {79.0X},
  MRNUMBER = {MR0065391 (16,426a)},
MRREVIEWER = {J. B. Diaz},
}

@book{m+f,
author="Morse, Philip and Feshbach, Herman",
title="Methods of theoretical physics, volume 1",
year={1953},
publisher="McGraw-Hill"
}

@book{m+f2,
author="Morse, Philip and Feshbach, Herman",
title="Methods of theoretical physics, volume 2",
year={1953},
publisher="McGraw-Hill"
}

@book{olver,
author="Olver, Frank W. J.",
title="Asymptotics and special functions",
year="1974",
publisher="Academic Press, New York"
}

@book{dlmf,
title="{NIST} Handbook of Mathematical Functions",
editor={Frank W. J. Olver and Daniel W. Lozier and Ronald F. Boisvert and Charles W. Clark},
publisher={Cambridge University Press},
year=2010
}

@book {watson,
author = {G N Watson},
title= {A Treatise on the Theory of {B}essel functions},
year = 1922,
publisher ={Cambridge University Press}
}

@book {rellichpert,
    AUTHOR = {Rellich, Franz},
     TITLE = {Perturbation theory of eigenvalue problems},
    SERIES = {Assisted by J. Berkowitz. With a preface by Jacob T. Schwartz},
 PUBLISHER = {Gordon and Breach Science Publishers},
   ADDRESS = {New York},
      YEAR = {1969},
     PAGES = {x+127},
   MRCLASS = {47.48},
  MRNUMBER = {MR0240668 (39 \#2014)},
}

@book{kato,
author={Kato, Tosio},
title="Perturbation Theory for Linear Operators",
publisher="Springer-Verlag",
address = {New York},
edition="2nd",
year=1976
}

@book {RSv1,
    AUTHOR = {Reed, Michael and Simon, Barry},
     TITLE = {Methods of modern mathematical physics. {I}. {F}unctional analysis},
   EDITION = {Second},
 PUBLISHER = {Academic Press Inc. [Harcourt Brace Jovanovich Publishers]},
   ADDRESS = {New York},
      YEAR = {1980},
     PAGES = {xv+400},
      ISBN = {0-12-585050-6},
   MRCLASS = {46-01 (47-01)},
  MRNUMBER = {MR751959 (85e:46002)},
}

@book {RSv4,
    AUTHOR = {Reed, Michael and Simon, Barry},
     TITLE = {Methods of modern mathematical physics. {IV}. {A}nalysis of
              operators},
 PUBLISHER = {Academic Press [Harcourt Brace Jovanovich Publishers]},
   ADDRESS = {New York},
      YEAR = {1978},
     PAGES = {xv+396},
      ISBN = {0-12-585004-2},
   MRCLASS = {47-02 (81.47)},
  MRNUMBER = {MR0493421 (58 \#12429c)},
MRREVIEWER = {P. R. Chernoff},
}


@book{debnath,
author={L Debnath and P Mikusinski},
title={Introduction to {H}ilbert Spaces with Applications},
publisher={Elsevier Science},
edition={3rd},
year=2005
}

@book{stein,
author="E. M. Stein",
title="Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals",
year=1993,
publisher="Princeton university press",
address="Princeton, NJ",
series="Monographs in Harmonic Analysis",
note="with the assistance of Timothy S. Murphy"
}

@article{cotlar,
author={M Cotlar},
title="A combinatorial inequality and its applications to ${L}^2$-spaces",
journal="Rev. Mat. Cuyana",
volume=1,
year=1955,
pages={41--55}
}

@article{Comech,
author= "A Comech",
title="Cotlar-{S}tein almost orthogonality lemma",
journal="preprint, http://www.\-math.tamu.edu/$\sim$comech/papers/CotlarStein/CotlarStein.pdf ",
year=2007
}

@book{strang,
author={G. Strang},
title="Introduction to Linear Algebra",
edition="4th Ed.",
year=2009
}

% -------------------------------- MATH EDUCATION

@misc{connectdots,
author={Kuh, G. D. and Kinzie, J. and Cruce, T. and Shoup, R. and Gonyea, R. M.},
year=2007,
title={Connecting the dots: Multi-faceted analyses of the relationships between student engagement results from the {NSSE}, and the institutional practices and conditions that foster student success},
note={Revised final report prepared for {\em {L}umina {F}oundation for {E}ducation}},
howpublished={\verb+http://nsse.iub.edu/pdf/Connecting_the_Dots_Report.pdf+}
}

@article{crouch,
author="C. H. Crouch and E. Mazur",
title={{P}eer {I}nstruction: Ten years of experience and results},
journal="Am.\ J.\ Phys.",
volume=69,
number=9,
year=2001,
pages={970--977}
}

@misc{cooplearning,
author="Johnson, D. and Johnson, R. and Stanne, M.",
year=2000,
note={Cooperative Learning Center, U. Minnesota},
title={Cooperative learning methods: A meta-analysis},
howpublished={{\tt http://www.co-operation.org/pages/cl-methods.html}}
}

@misc{demospositiveimpact,
year=2006,
title={Demos with Positive Impact},
note="{\tt http://mathdemos.gcsu.edu/}",
author={David R. Hill and Lila F. Roberts}
}

@article{farrell,
author={Farrell, E. F.},
year=2002,
title="Engineering a warmer welcome for female students",
journal={The Chronicle of Higher Education},
volume=48,
pages={A31}
}


% end


